Question

Given the function f(x) = 2-4, determine the slope of the tangent line of f at
x = -1 using the limit shown below. You do not have to simplify your answer.

Answer 1

Answer:

Slope of the tangent line at x=-1

$(\frac{dy}{dx})_{x=-1} = e^{-5}$

Step-by-step explanation:

Explanation:-

Given function

                            y = f(x) = e ˣ⁻⁴  ...(i)

       Differentiating equation (i) with respective to 'x' , we get

                         $\frac{dy}{dx} = e^{x-4} \frac{d}{dx} (x-4)$

                       $\frac{dy}{dx} = e^{x-4} (1)$

Slope of the tangent line

                       $(\frac{dy}{dx})_{x=-1} = e^{-1-4} = e^{-5}$