Question

The point in the interval [0, 2p] where f(x) = e^x sin x has maximum slope is

• A. $\frac{\pi}{4}$
• B. $\frac{\pi}{2}$
• C. p
• D. None of these

Answer 1

Answer: (B)

$\frac{\pi}{2}$

Answer 2

Slope m = f '(x) = e^xsinx + e^xcosx

= e^x(sinx + cos x)

$\frac{dm}{dx}$= e^x (sinx + cosx) + e^x (cos x – sin x)

= e^x (2cosx)