Question

use the chart to find h(2) in simplest form.

x	f(x)	f(x)	g(x)	g(x)
2	9	12	3	-7

h(x)=\frac{f(x)}{g(x)}
answer attempt 1 out of 2
h(2)=

Explanation:

Step1: Recall quotient - rule

The quotient - rule states that if $h(x)=\frac{f(x)}{g(x)}$, then $h^{\prime}(x)=\frac{f^{\prime}(x)g(x)-f(x)g^{\prime}(x)}{[g(x)]^{2}}$.

Step2: Substitute $x = 2$

When $x = 2$, we substitute the values from the table: $f(2)=9$, $f^{\prime}(2)=12$, $g(2)=3$, and $g^{\prime}(2)=-7$ into the quotient - rule formula.
$h^{\prime}(2)=\frac{f^{\prime}(2)g(2)-f(2)g^{\prime}(2)}{[g(2)]^{2}}$.

Step3: Calculate the numerator

$f^{\prime}(2)g(2)-f(2)g^{\prime}(2)=12\times3 - 9\times(-7)=36 + 63=99$.

Step4: Calculate the denominator

$[g(2)]^{2}=3^{2}=9$.

Step5: Find $h^{\prime}(2)$

$h^{\prime}(2)=\frac{99}{9}=11$.

Answer:

$11$