Question

question
find slope of the line tangent to the graph of $f(x)=x^{3}-4x + 2$ at $x = 2$.
provide your answer below:
slope = □

Explanation:

Step1: Find the derivative of the function

The derivative of $f(x)=x^{3}-4x + 2$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $f^\prime(x)=3x^{2}-4$.

Step2: Evaluate the derivative at the given point

Substitute $x = 2$ into $f^\prime(x)$. So $f^\prime(2)=3\times(2)^{2}-4$.
First, calculate $(2)^{2}=4$. Then $3\times4-4=12 - 4=8$.

Answer:

$8$