Explanation
We are given the following function:
[tex]f(x)=3\cos2x[/tex]
We are required to determine the instantaneous rate of change at x = 2π.
This is achieved thus:
[tex]\begin{gathered} f(x)=3\cos2x \\ \frac{\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}[/tex]
Hence, the answer is:
[tex]\frac{\operatorname{\triangle}f(x)}{\operatorname{\triangle}x}=0[/tex]
