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Problem 50 Medium Difficulty

Let $ P(x) = F(x)G(x) $ and $ Q(x) = F(x)/G(x), $ where $ F $ and $ G $ are the functions whose graphs are shown.
(a) Find $ P'(2). $
(b) Find $ Q'(7). $

Answer

(a) $\frac{3}{2}$
(b) $\frac{43}{12}$

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Video Transcript

Explorer. So when you read here, so for part A, we're first on apply the product world when we get the derivative of, uh, times the derivative of G plus the derivative of half times the derivative of G. We plug in to for X. When we get the derivative of P up to is equal to zero times two plus three times 0.5, which becomes equal to three halves. Report be we're gonna applied the quotient bull. So we have y is equal to you over B. That means the derivative of Y is equal to three times the derivative of you. Minus you turns the derivative of B over the square. So cue the derivative of Q is equal to G of X owns the derivative of X miners of X times, the derivative of G of X, all over G of X Square. Re plug in seven for X, and we get one times 1/4 minus five times negative 2/3 over one square, which is equal to 43 over 12