calculus

A function f is defined on the interval [0,4], and its derivative is e^sinx-2cos3x

a. on what interval is f increasing?
b. at what value(s) of x does f have a local maxima?
c. how many points of inflection does f have?

*calculator is allowed for this problem

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  1. a. f is increasing where f' > 0
    So, where do you have e^sinx-2cos3x > 0 ?

    b. you need e^sinx-2cos3x = 0

    c. points of inflection are where f" = 0
    f" = (e^sinx)(cosx) + 6sin3x
    so, where is that zero?

    you can check your answers at wolframalpha.com
    The graph of e^sinx-2cos3x on [0,4] can be seen at

    https://www.wolframalpha.com/input/?i=e%5Esinx-2cos3x+where+0+%3C%3D+x+%3C%3D+4

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    oobleck

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