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Math Help - finding y = f(x)

  1. #1
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    finding y = f(x)

    Lost on this problem:

    Find y = f(x) given f^ii(x) = 12x^2 and f^i (1) = 10 and f(2) = 26
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dasani View Post
    Lost on this problem:

    Find y = f(x) given f^ii(x) = 12x^2 and f^i (1) = 10 and f(2) = 26
    How long did you try to figure this out?

    f''(x) = 12x^2

    \Rightarrow f'(x) = \int f''(x)~dx = 12 \int x^2 ~dx = 4x^3 + C

    Now f'(1) = 10

    \Rightarrow 10 = 4(1)^3 + C \implies C = 6

    So, f'(x) = 4x^3 + 6



    \Rightarrow f(x) = \int f'(x)~dx = \int \left( 4x^3 + 6 \right)~dx = x^4 + 6x + C

    Now f(2) = 26

    \Rightarrow 26 = (2)^4 + 6(2) + C \implies C = -2

    So, finally, \boxed { f(x) = x^4 + 6x - 2 }
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  3. #3
    MHF Contributor red_dog's Avatar
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    \displaystyle f''(x)=12x^2\Rightarrow f'(x)=12\cdot \frac{x^3}{3}+c_1=4x^3+c_1
    f'(1)=10\Rightarrow 4+c_1=10\Rightarrow c_1=6\Rightarrow f'(x)=4x^3+6
    \displaystyle \Rightarrow f(x)=4\cdot \frac{x^4}{4}+6x+c_2=x^4+6x+c_2
    f(2)=26\Rightarrow c_2=-2\Rightarrow f(x)=x^4+6x-2
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  4. #4
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    I've been working on these problems since yesterday...We haven't covered this chapter in class so I'm basically teaching myself, which is why I am so confused about it.
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