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Math Help - calc function question

  1. #1
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    calc function question

    The function f has a relative maximum value of 3 at x=1, as shown in the figure above. If h(x)=x^2f(x), then h'(1)=

    It gives me a graph that i drew below..Do I need to find the function equation of f(x) first? If so how would I do that? thanks for the help.
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  2. #2
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    Quote Originally Posted by jst706 View Post
    The function f has a relative maximum value of 3 at x=1, as shown in the figure above. If h(x)=x^2f(x), then h'(1)=

    It gives me a graph that i drew below..Do I need to find the function equation of f(x) first? If so how would I do that? thanks for the help.
    Hello,

    I assume that the function h is: h(x) = x^2 \cdot f(x). If so use the product rule to calculate the derivative:

    h'(x) = f(x) \cdot 2x + x^2 \cdot f'(x)

    You know already:
    f(1) = 3
    f'(1) = 0
    Substitute these values into the equation of the drivative:

    h'(1) = 3 \cdot 2 + 1^2 \cdot 0 = 6
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  3. #3
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    thanks a lot...very well explained...one quick question though..f'(1)=0 because the derivative of three is 0 correct?
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  4. #4
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    Quote Originally Posted by jst706 View Post
    thanks a lot...very well explained...one quick question though..f'(1)=0 because the derivative of three is 0 correct?
    Hi,

    as you may know a function has an extremum (maximum or minimum) if the first derivative is zero. Thus you know if a function has a maximum at x = 1 the drivative at x = 1 must be zero.
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