Question

for the function $f(x)=4x^{2}+11x + 7$, find the slope of the tangent line at $x=-6$.

Explanation:

Step1: Find the derivative

The derivative of $f(x)=4x^{2}+11x + 7$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $f^\prime(x)=8x+11$.

Step2: Evaluate the derivative at $x=-6$

Substitute $x = - 6$ into $f^\prime(x)$: $f^\prime(-6)=8\times(-6)+11$.
$f^\prime(-6)=-48 + 11=-37$.

Answer:

$-37$