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AP微积分AB:点导数

学习AP微积分AB的概念、例题和解释

创建帐户制作测试和抽认卡

所有AP微积分AB资源

3诊断测试 164实践测试今日问题抽认卡从概念中学习

例子问题

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问题42:A点导数

求函数的切线斜率

$g(x)=x^2\cos(x)$

在 $x=\pi$

可能的答案:

$\pi$

$2\pi$

$-2\pi$

正确答案:

$-2\pi$

解释：

函数的切线斜率就是一阶导数，对于这个函数等于

$g'(x)=2x\cos(x)-x^2\sin(x)$

使用以下规则发现:

$\frac{\mathrm{d} }{\mathrm{d} x} f(x)g(x)=f'(x)g(x)+f(x)g'(x)$ ， $\frac{\mathrm{d} }{\mathrm{d} x} \cos(x)=-\sin(x)$ ， $\frac{\mathrm{d} }{\mathrm{d} x} x^n=nx^{n-1}$

在给定点处求值，我们得到切线的斜率等于

$g'(\pi)=2\pi(\cos(\pi))-\pi^2(\sin(\pi))=-2\pi$

报告错误

问题43:A点导数

Functionplot

$\begin{align*}&\text{Determine the sign of the derivative of the function above at the point }\\&x=2\end{align*}$

可能的答案:

$\text{The derivative is positive.}$

$\text{The derivative is negative.}$

$\text{The derivative is zero.}$

正确答案:

$\text{The derivative is positive.}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=2\text{, the function appears to be increasing.}\\&\text{The derivative is positive.}\end{align*}$

报告错误

问题44:A点导数

Functionplot

$\begin{align*}&\text{Determine the sign of the derivative of the function above at the point }\\&x=4\end{align*}$

可能的答案:

$\text{The derivative is negative.}$

$\text{The derivative is positive.}$

$\text{The derivative is zero.}$

正确答案:

$\text{The derivative is negative.}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=4\text{, the function appears to be decreasing.}\\&\text{The derivative is negative.}\end{align*}$

报告错误

问题45:A点导数

Functionplot

$\begin{align*}&\text{Determine the sign of the derivative of the function above at the point }\\&x=3\end{align*}$

可能的答案:

$\text{The derivative is negative.}$

$\text{The derivative is zero.}$

$\text{The derivative is positive.}$

正确答案:

$\text{The derivative is positive.}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=3\text{, the function appears to be increasing.}\\&\text{The derivative is positive.}\end{align*}$

报告错误

问题46:A点导数

Functionplot

$\begin{align*}&\text{Determine the sign of the derivative of the function above at the point }\\&x=-0.3\end{align*}$

可能的答案:

$\text{The derivative is negative.}$

$\text{The derivative is zero}$

$\text{The derivative is positive.}$

正确答案:

$\text{The derivative is zero}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=-0.3\text{, the function appears to be flat.}\\&\text{The derivative is zero}\end{align*}$

报告错误

问题47:A点导数

Functionplot

$\begin{align*}&\text{Determine the sign of the derivative of the function above at the point }\\&x=0.2\end{align*}$

可能的答案:

$\text{The derivative is zero}$

$\text{The derivative is negative.}$

$\text{The derivative is positive.}$

正确答案:

$\text{The derivative is zero}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=0.2\text{, the function appears to be flat.}\\&\text{The derivative is zero}\end{align*}$

报告错误

问题141:Ap微积分Ab

Functionplot

$\begin{align*}&\text{Determine whether or not the derivative of the function above at the point }\\&x=-1\\&\text{is positive, negative, or zero.}\end{align*}$

可能的答案:

$\text{The derivative is zero.}$

$\text{The derivative is negative.}$

$\text{The derivative is positive.}$

正确答案:

$\text{The derivative is negative.}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=-1\text{, the function appears to be decreasing.}\\&\text{The derivative is negative.}\end{align*}$

报告错误

问题49:A点导数

Functionplot

$\begin{align*}&\text{Determine whether or not the derivative of the function above at the point }\\&x=-1\\&\text{is positive, negative, or zero.}\end{align*}$

可能的答案:

$\text{The derivative is zero.}$

$\text{The derivative is negative.}$

$\text{The derivative is positive.}$

正确答案:

$\text{The derivative is positive.}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=-1\text{, the function appears to be increasing.}\\&\text{The derivative is positive.}\end{align*}$

报告错误

问题141:衍生品

Functionplot

$\begin{align*}&\text{Determine whether or not the derivative of the function above at the point }\\&x=7\\&\text{is positive, negative, or zero.}\end{align*}$

可能的答案:

$\text{The derivative is zero.}$

$\text{The derivative is negative.}$

$\text{The derivative is positive.}$

正确答案:

$\text{The derivative is positive.}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=7\text{, the function appears to be increasing.}\\&\text{The derivative is positive.}\end{align*}$

报告错误

问题51:A点导数

Functionplot

$\begin{align*}&\text{Conclude if the derivative of the function above at the point }\\&x=3\\&\text{is positive, negative, or zero.}\end{align*}$

可能的答案:

$\text{The derivative is zero.}$

$\text{The derivative is positive.}$

$\text{The derivative is negative.}$

正确答案:

$\text{The derivative is positive.}$

解释：

$\begin{align*}&\text{The derivative of a function at a given point is synonymous}\\&\text{with the slope of a function at a given point. Therefore if}\\&\text{the function increases in value as x increases across a point,}\\&\text{the slope and derivative are positive. Conversely, if the function}\\&\text{decreases in value as x increases across a point, both slope}\\&\text{and derivative are negative. At points where the function is}\\&\text{flat, the slope and derivative are zero.}\\&\text{Studying the slope at }x=3\text{, the function appears to be increasing.}\\&\text{The derivative is positive.}\end{align*}$

报告错误

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查看AP微积分AB导师

不
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刘易斯堡学院，学士，数学，地质学。弗吉尼亚理工学院和州立大学，地球科学博士。

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Damion
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圣爱德华大学，会计学学士。德克萨斯大学奥斯汀分校会计学硕士。

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尼娜
认证导师

普林斯顿大学，计算机科学学士。

所有AP微积分AB资源

3诊断测试 164实践测试今日问题抽认卡从概念中学习

受欢迎的科目

华盛顿特区的LSAT导师，休斯顿的LSAT导师，凤凰城的计算机科学导师，洛杉矶的LSAT导师，迈阿密的SAT家教，圣地亚哥的ACT导师，达拉斯沃斯堡的数学导师，洛杉矶的化学导师，达拉斯沃斯堡的代数导师，休斯顿的ISEE导师

常用备考

在凤凰城准备LSAT考试，在迈阿密准备GMAT考试，ISEE考试准备在休斯顿，MCAT考试准备在华盛顿特区，MCAT考试准备在洛杉矶，SSAT考试准备在旧金山湾区，费城SSAT考试准备中心，在休斯顿准备SAT考试，费城LSAT考试准备中心，在芝加哥准备ACT考试

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AP微积分AB:点导数

学习AP微积分AB的概念、例题和解释

所有AP微积分AB资源

例子问题

问题42:A点导数

问题43:A点导数

问题44:A点导数

问题45:A点导数

问题46:A点导数

问题47:A点导数

问题141:Ap微积分Ab

问题49:A点导数

问题141:衍生品

问题51:A点导数

所有AP微积分AB资源

报告与此问题有关的问题

DMCA的抱怨

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