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FacePalm · Answer 1 · 2023-08-26T14:34:53+0000

Explanation

We are given the following function:

$f(x)=3\cos2x$

We are required to determine the instantaneous rate of change at x = 2π.

This is achieved thus:

$\begin{gathered} f(x)=3\cos2x \\ (\triangle f(x))/(\triangle x)=3\cdot-2\sin2x \\ \frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=-6\sin2x \\ \text{ At the point }x=2\pi \\ \frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=0 \end{gathered}$

Hence, the answer is:

$\frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=0$

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