Question

Asked Mar 5, 2019

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Let h(x)=f(x)/g(x), where f(−3)=7,f′(−3)=−9,g(−3)=−2, and g′(−3)=1. What is h′(−3)?

Do not include "h′(−3)=" in your answer. For example, if you found h′(−3)=20, you would enter 20.

Step 1

h(x) = f(x) / g(x)

Hence, h'(x) =[g(x)f'(x) - f(x).g'(x)] / [g(x)]^{2}

Step 2

At x = 3, f(−3)=7,f′(−3)=−9,g(−3)=−2, and g′(−3)=1

Hence, h'(-3) = [g(-3)f'(-3) - f(-3)g'(-3)] / [g(-3)]2 = [-2 x (-9) - 7 x 1] / (-2)2 = 11 / 4

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