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Math Help - Need answer

  1. #1
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    Need answer

    If g'(3) = 4 and h'(3) = -1 , find f '(3) for f(x) = 5g(x) + 3h(x) + 2
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  2. #2
    Super Member angel.white's Avatar
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    Quote Originally Posted by ArmiAldi View Post
    If g'(3) = 4 and h'(3) = -1 , find f '(3) for f(x) = 5g(x) + 3h(x) + 2
    Initial equation
    f(x) ~~=~~ 5~g(x) ~~+~~ 3~h(x)

    Take the derivative
    \frac{d}{dx}[ ~f(x)~] ~~=~~ \frac{d}{dx}[~5~g(x) ~~+ ~~3~h(x)~]

    Split the derivative on the right side
    \frac{d}{dx}[ ~f(x)~] ~~=~~ \frac{d}{dx}[~5~g(x)~] ~~+ ~~\frac{d}{dx}[~3~h(x)~]

    Pull coefficients out
    \frac{d}{dx}[ ~f(x)~] ~~=~~ 5~\frac{d}{dx}[~g(x)~] ~~+ ~~3~\frac{d}{dx}[~h(x)~]

    Switch to Newtonian notation (use a slash for prime instead of d/dx)
    f\prime (x) ~~=~~ 5~g\prime(x) ~~+~~ 3~h\prime (x)

    Now plug in x=3
    f\prime (3) ~~=~~ 5~g\prime(3) ~~+~~ 3~h\prime (3)

    And substitute your answers with the data given to you
    f\prime (3) ~~=~~ 5(4) ~~+~~ 3(-1)

    And simplify
    f\prime (3) ~~=~~ 17
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