Question

The first derivative of the function f is given by f '(x)=x-4e^(sin(2x)). How many points of inflection does the graph of f have on the interval 0≤x≤2π

Answer 1

Get f''(x) and let this be equal to 0. Count the number of solutions in the indicated interval.

Answer 2

Can you please tell me what the derivative is

Answer 3

\[f''(x)=(f'(x))'=1-8\cos(2x)e^{\sin{2x}}\\
f''(x)=0 \Leftrightarrow \cos(2x)e^{\sin{2x}}=\frac{1}{8} \]