Question

for the function $f(x)=x^{2}-7$, find the slope of the tangent line at $x = - 12$.

Explanation:

Step1: Find the derivative

The derivative of $f(x)=x^{2}-7$ using the power - rule $\frac{d}{dx}(x^n)=nx^{n - 1}$ is $f^\prime(x)=2x$.

Step2: Evaluate the derivative at $x=-12$

Substitute $x = - 12$ into $f^\prime(x)$. So $f^\prime(-12)=2\times(-12)$.

Answer:

$-24$