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Math Help - Finding a and b (derivatives)

  1. #1
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    Finding a and b (derivatives)

    What are the values that a and b can take so that f(x)= ax^2 + bx -sin3x has a local maximum when x=0 ?

    Thanks in advance
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  2. #2
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    Quote Originally Posted by sebasto View Post
    What are the values that a and b can take so that f(x)= ax^2 + bx -sin3x has a local maximum when x=0 ?

    Thanks in advance
    To have a local max at zero

    f'(0)=0 and f''(0) < 0

    Using these two gives

    f'(x)=2ax+b-3\cos(3x) \implies f(0)=0=b -3 \implies b=3

    f''(x)=2a+9\sin(3x) \implies f''(0)=2a \implies 2a < 0 \iff a < 0

    So this function has a max at zero anytime a < 0 \mbox{ and } b=3

    Here is a graph with a=-1 (black),-3 (red) ,-5 (blue)

    Finding a and b (derivatives)-max.bmp
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