question let $h(x)=f(x)+g(x)$. if $f(x)=x^{2}$ and $g(x)=2x$, what is $h(-2)$? do not include \$h(-2)=$\ in…

question let $h(x)=f(x)+g(x)$. if $f(x)=x^{2}$ and $g(x)=2x$, what is $h(-2)$? do not include \$h(-2)=$\ in your answer. for example, if you found $h(-2)$ provide your answer below:

question let $h(x)=f(x)+g(x)$. if $f(x)=x^{2}$ and $g(x)=2x$, what is $h(-2)$? do not include \$h(-2)=$\ in your answer. for example, if you found $h(-2)$ provide your answer below:

Answer

Explanation:

Step1: Find the function h(x)

Since (h(x)=f(x) + g(x)), and (f(x)=x^{2}), (g(x)=2x), then (h(x)=x^{2}+2x).

Step2: Differentiate h(x)

Using the power - rule ((x^{n})^\prime=nx^{n - 1}), the derivative (h^\prime(x)=(x^{2}+2x)^\prime=(x^{2})^\prime+(2x)^\prime = 2x + 2).

Step3: Evaluate h'(-2)

Substitute (x=-2) into (h^\prime(x)): (h^\prime(-2)=2\times(-2)+2=-4 + 2=-2).

Answer:

-2