Question

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:

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