find the instantaneous rate of change for the function at the given value. f(x)=x^2 + 4x at x = - 1 the…

find the instantaneous rate of change for the function at the given value. f(x)=x^2 + 4x at x = - 1 the instantaneous rate of change at x = - 1 is

find the instantaneous rate of change for the function at the given value. f(x)=x^2 + 4x at x = - 1 the instantaneous rate of change at x = - 1 is

Answer

Explanation:

Step1: Find the derivative of the function

The derivative of $f(x)=x^{2}+4x$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $f^\prime(x)=\frac{d}{dx}(x^{2})+\frac{d}{dx}(4x)=2x + 4$.

Step2: Evaluate the derivative at the given point

Substitute $x=-1$ into $f^\prime(x)$. So $f^\prime(-1)=2(-1)+4$. $f^\prime(-1)=-2 + 4=2$.

Answer:

$2$