Question

question use the chart to find h(5) in simplest form. x f(x) f(x) g(x) g(x) 5 -5 -11 11 7 11 2 -12 -3 -8 h(x)=f(g(x)) answer attempt 1 out of 2 h(5)=

Explanation:

Step1: Apply chain - rule

The chain - rule states that if $h(x)=f(g(x))$, then $h^{\prime}(x)=f^{\prime}(g(x))\cdot g^{\prime}(x)$. So, $h^{\prime}(5)=f^{\prime}(g(5))\cdot g^{\prime}(5)$.

Step2: Find $g(5)$ and $g^{\prime}(5)$ from the table

From the table, when $x = 5$, $g(5)=11$ and $g^{\prime}(5)=7$.

Step3: Find $f^{\prime}(g(5))$

Since $g(5)=11$, we need to find $f^{\prime}(11)$. From the table, when $x = 11$, $f^{\prime}(11)=-12$.

Step4: Calculate $h^{\prime}(5)$

$h^{\prime}(5)=f^{\prime}(g(5))\cdot g^{\prime}(5)=f^{\prime}(11)\cdot7=-12\times7=-84$.

Answer:

$-84$