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

Slope of the tangent line at x=-1

`((dy)/(dx))_(x=-1) = e^(-5)`

Explanation:

Explanation:-

Given function

y = f(x) = e ˣ⁻⁴ ...(i)

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

`(dy)/(dx) = e^(x-4) (d)/(dx) (x-4)`

`(dy)/(dx) = e^(x-4) (1)`

Slope of the tangent line

`((dy)/(dx))_(x=-1) = e^(-1-4) = e^(-5)`