Question

If f(x) = e2x + e1 − x, what is the slope of the tangent line of f(x) at x = 0?

1 + e
1 – e
2 + e
2 – e

Answer 1

The slope of the tangent line to the function f(x) = e2x + e1 - x at x = 0 is 2 - e.

Step-by-step explanation:

The student is asking for the slope of the tangent line to the function f(x) = e2x + e1 - x at x = 0. To find this, we need to determine the derivative of f(x), which will give us the slope of the tangent line at any point x, and then evaluate it at x = 0.

First, let's find the derivative of f(x) using the sum and chain rule:

f'(x) = d/dx(e2x) + d/dx(e1 - x)
= 2e2x - e1 - x

Now let's evaluate the derivative at x = 0:

f'(0) = 2e2(0) - e1 - 0
= 2e0 - e1
= 2(1) - e
= 2 - e

So the slope of the tangent line at x = 0 is 2 - e.