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Math Help - Fund. Thm of Calc Question

  1. #1
    Senior Member polymerase's Avatar
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    Fund. Thm of Calc Question

    Let G(x)=\int^{2x}_{3x}\;f(t)\:dt, where f(t)=\int^{2-t}_{2t-5}\sqrt{1+u^4}\;du. Then G''(1)=
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  2. #2
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    Quote Originally Posted by polymerase View Post
    Let G(x)=\int^{2x}_{3x}\;f(t)\:dt, where f(t)=\int^{2-t}_{2t-5}\sqrt{1+u^4}\;du. Then G''(1)=
    As a start, G^{'}(x) = 2 f(2x) - 3 f(3x).

    So now you need to differentiate 2 f(2x) - 3 f(3x) with respect to x, where you know the rule for f ........
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  3. #3
    Senior Member polymerase's Avatar
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    Quote Originally Posted by mr fantastic View Post
    As a start, G^{'}(x) = 2 f(2x) - 3 f(3x).

    So now you need to differentiate 2 f(2x) - 3 f(3x) with respect to x, where you know the rule for f ........
    what do you do now?
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  4. #4
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    Quote Originally Posted by polymerase View Post
    what do you do now?
    Indeed, what do you do now?

    At the risk of sounding arrogant, I would have thought it was reasonably obvious that now you get expressions for f(2x) and f(3x) using the given rule f(t)=\int^{2-t}_{2t-5}\sqrt{1+u^4}\;du.

    Then you construct the expression 2f(2x) - 3f(3x). Then you differentiate it.
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