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Math Help - Find value of second derivative when you don't know the first function

  1. #1
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    Find value of second derivative when you don't know the first function

    I'm not to sure i understand this.. i think i did it right but am unsure...

    If f(2) = 1 and f'(x) = x^2f(x) for all x , find f''(2)

    This is what I did:

    f''(x) = 2xf(x)
    f''(2) = 2(2)(1) = 4

    This just seems too easy to be true hah
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  2. #2
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    Re: Find value of second derivative when you don't know the first function

    Quote Originally Posted by tmas View Post
    I'm not to sure i understand this.. i think i did it right but am unsure...
    If f(2) = 1 and f'(x) = x^2f(x) for all x , find f''(2)
    This is what I did:
    f''(x) = 2xf(x) Incorrect
    f' is a product.

    f"(x)=2xf(x)+x^2f'(x)
    Thanks from tmas
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