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Math Help - find f given f"

  1. #1
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    find f given f"

    Find f. f ''(t) = 4/√t
    f(4) = 22
    f '(4) = 5

    f"= 4t^{-1/2}
    f'=2(4)t^{1/2} +C
    f'(4)=16+C=5
    C=-11

    so f'= f'=8^{1/2} -11t
    f=(2)\frac{8t^{3/2}}{3} -\frac{11t^2}{2}+D

    f(4)=(2)\frac{8(4)^{3/2}}{3} -\frac{11(4)^2}{2}+D=22

    f(4)=\frac{16(8)}{3} -\frac{11(16)}{2}+D=22

    f(4)=\frac{128}{3} -88+D=22

    f(4)=\frac{128}{3} +D=110

    f(4)=\frac{128}{3} +D=\frac{330}{10}
    <br />
D=\frac{202}{3}

    I got this, but it was wrong: f(t)=
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  2. #2
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    Quote Originally Posted by hazecraze View Post
    Find f. f ''(t) = 4/√t
    f(4) = 22
    f '(4) = 5

    f"= 4t^{-1/2}
    f'=2(4)t^{1/2} +C
    f'(4)=16+C=5
    C=-11 <<<<<< OK

    so f'= f'=8\bold{\color{red}t}^{1/2} -11
    ...
    1. According to your calculations:

    f'(t)=8t^{\frac12}-11

    2. f(t)=\frac23 \cdot 8 t^{\frac32} - 11t + c

    3. Now f(4) = 22

    Plug in this value to calculate c.

    I've got c = \frac{166}3
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