Question

question: find slope of the line tangent to the graph of f(x)=x^3 - 4x^2+2 at x = 1. write your answer below.

Explanation:

Step1: Find the derivative of $f(x)$

The derivative of $f(x)=x^{3}-4x^{2}+2$ using the power - rule $\frac{d}{dx}(x^{n})=nx^{n - 1}$ is $f'(x)=3x^{2}-8x$.

Step2: Evaluate the derivative at $x = 1$

Substitute $x = 1$ into $f'(x)$. So $f'(1)=3(1)^{2}-8(1)=3 - 8=-5$.

Answer:

$-5$