Determining the slope of the function

Question

Determine the slope of the function $f(x)=-6xe^{-2x}$ at the point with x-coordinate $x=\frac 12$ and what occurs there

What is the equation of the tangent line at the point with $x$-coordinate $x=\frac 12$

Does anyone know the answers for these

Answer 1

Use product rule to differentiate this $$f'(x)=-6e^{-2x} + 12xe^{-2x}$$

To find the equation of tangent follow these steps:

1) Find the first derivative of $f(x)$.

2) Plug $x$ value of the indicated point into $f '(x)$ to find the slope at $x$.

3) Plug $x$ value into $f(x)$ to find the $y$ coordinate of the tangent point.

4) Combine the slope from step $2$ and point from step $3$ using the point-slope formula to get the equation for the tangent line.