A function f is defined on the interval [0,4], and it's derivative is f'(x) = e^sinx - 2cos3x

(a) On what interval is f increasing? Justify your answer
(b) At what value(s) of x does f have local maxima? Justify your answer.
(c) How many points of inflection does that graph of f have? Justify your answer.

Question

A function f is defined on the interval [0,4], and it's derivative is f'(x) = e^sinx - 2cos3x

(a) On what interval is f increasing? Justify your answer
(b) At what value(s) of x does f have local maxima? Justify your answer.
(c) How many points of inflection does that graph of f have? Justify your answer.

richyw · Answer

(a) on the interval  where $f'(x)>0$
(b) it can only be a local maxima where $f'(x)=0$. This is necessary but not sufficient to show that it is.
(c)inflection points can occur where $f''(x)=0$. Again this is necessary but not sufficient