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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.
(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