Question

Gr 12 calcFind the critical points on the given interval and identify the nature of them

Answer 1

The critical point is the point where the derivative of the function is equal to zero or undefined.

So, for

`f(x)=2^xcos(x)\text{ }`

the derivative becomes

`\begin{gathered} (d)/(dx)(2^xcos(x)) \\ apply\text{ the product rule} \\ (d)/(dx)(2^x)cos(x)+(d)/(dx)(cos(x))2^x \\ 2^xln(2)cos(x)+(-sin(x))(2^x) \\ =ln(2)2^xcos(x)-2^xsin(x) \end{gathered}`

Setting the derivative to zero, we have