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    Monoxdifly's Avatar
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    #1
    If $ \displaystyle f(x)=\frac{3x^2-5}{x+6}$ then f(0) + f'(0) is ....
    A. 2
    B. 1
    C. 0
    D. -1
    E. -2

    What I did:
    If $ \displaystyle f(x)=\frac{u}{v}$ then:
    u =$ \displaystyle 3x^2-5$ → u' = 6x
    v = x + 6 → v' = 1
    f'(x) =$ \displaystyle \frac{u'v-uv'}{v^2}$=$ \displaystyle \frac{6x(x+6)-(3x^2-5)(1)}{(x+6)^2}$
    f(0) + f'(0) = $ \displaystyle \frac{3(0^2)-5}{0+6}$ + $ \displaystyle \frac{6(0)(0+6)-(3(0^2)-5)(1)}{(0+6)^2}$ = $ \displaystyle \frac{3(0)-5}{6}$ + $ \displaystyle \frac{0(0+6)-(3(0)-5)}{6^2}$= $ \displaystyle \frac{0-5}{6}$ + $ \displaystyle \frac{0-(0-5)}{36}$ = $ \displaystyle \frac{-5}{6}$ + $ \displaystyle \frac{0-(-5)}{36}$ = $ \displaystyle \frac{-30}{36}$ + $ \displaystyle \frac{0+5}{36}$ = $ \displaystyle \frac{-25}{36}$
    The answer isn't in any of the options. I did nothing wrong, right?

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    Opalg's Avatar
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    #2
    Quote Originally Posted by Monoxdifly View Post
    If $ \displaystyle f(x)=\frac{3x^2-5}{x+6}$ then f(0) + f'(0) is ....
    A. 2
    B. 1
    C. 0
    D. -1
    E. -2

    What I did:
    If $ \displaystyle f(x)=\frac{u}{v}$ then:
    u =$ \displaystyle 3x^2-5$ → u' = 6x
    v = x + 6 → v' = 1
    f'(x) =$ \displaystyle \frac{u'v-uv'}{v^2}$=$ \displaystyle \frac{6x(x+6)-(3x^2-5)(1)}{(x+6)^2}$
    f(0) + f'(0) = $ \displaystyle \frac{3(0^2)-5}{0+6}$ + $ \displaystyle \frac{6(0)(0+6)-(3(0^2)-5)(1)}{(0+6)^2}$ = $ \displaystyle \frac{3(0)-5}{6}$ + $ \displaystyle \frac{0(0+6)-(3(0)-5)}{6^2}$= $ \displaystyle \frac{0-5}{6}$ + $ \displaystyle \frac{0-(0-5)}{36}$ = $ \displaystyle \frac{-5}{6}$ + $ \displaystyle \frac{0-(-5)}{36}$ = $ \displaystyle \frac{-30}{36}$ + $ \displaystyle \frac{0+5}{36}$ = $ \displaystyle \frac{-25}{36}$
    The answer isn't in any of the options. I did nothing wrong, right?
    Your calculation is correct, and the answer is not one of the listed options. Maybe you should check whether you read the question correctly.

  4. MHB Master
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    #3
    Yes, the correct answer is $ \displaystyle -\frac{25}{36}$.

  5. MHB Craftsman
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    #4 Thread Author
    OK, thanks for the clarifications...

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