Suppose f(x)=α(x)β(x)γ(x) for every real x, where α(x), β(x), and γ(x) are differentiable. If f'(2)=18f(2), α'(2)=3α(2), β'(2)=-4β(2), and γ'(2)=kγ(2), then what is the value of k?

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Accepted Answer

19. Logarithmic differentiation: f'(2)/f(2)=a'/a+b'/b+g'/g = 3+(-4)+k = 18, so k=19.

Suppose f(x)=α(x)β(x)γ(x) for every real x, where α(x), β(x), and γ(x) are differentiable. If f'(2)=18f(2), α'(2)=3α(2), β'(2)=-4β(2), and γ'(2)=kγ(2), then what is the value of k?

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