Question

find the instantaneous rate of change for the function at the given value.
f(x)=x^{2}+3x at x = - 1
the instantaneous rate of change at x = - 1 is

Explanation:

Step1: Find the derivative of the function

The derivative of $f(x)=x^{2}+3x$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $f^\prime(x)=\frac{d}{dx}(x^{2})+\frac{d}{dx}(3x)=2x + 3$.

Step2: Evaluate the derivative at the given point

Substitute $x=-1$ into $f^\prime(x)$. So $f^\prime(-1)=2(-1)+3$.
$f^\prime(-1)=-2 + 3=1$.

Answer:

$1$