Mathematics
FernandaReistad58
11

suppose that f(pi/3)=4 and f'(pi/3)=-2, and let g(x)= (cosx)/f(x). find g'(x) (pi/3)

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(1) Answers
CollinsLeeHinch

[latex]g(x)=\dfrac{\cos x}{f(x)}[/latex] [latex]\implies g'(x)=-\dfrac{f(x)\sin x+f'(x)\cos x}{f(x)^2}[/latex] You know that [latex]f\left(\dfrac\pi3\right)=4[/latex] and [latex]f'\left(\dfrac\pi3\right)=-2[/latex], so [latex]g'\left(\dfrac\pi3\right)=-\dfrac{4\sin\frac\pi3-2\cos\frac\pi3}{4^2}=\dfrac{1-2\sqrt3}{16}[/latex]

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