Question

question 16 · 1 point. let (h(x)=\frac{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. provide your answer below:

Explanation:

Step1: Apply quotient - rule

$h'(x)=\frac{f'(x)g(x)-f(x)g'(x)}{g(x)^2}$

Step2: Substitute $x = - 3$

$h'(-3)=\frac{f'(-3)g(-3)-f(-3)g'(-3)}{g(-3)^2}$

Step3: Plug in values

$h'(-3)=\frac{(-9)\times(-2)-7\times1}{(-2)^2}=\frac{18 - 7}{4}=\frac{11}{4}=2.75$

Answer:

$2.75$