Question

What is the slope of `f(x)=-e^x+2x` at `x=1`?

Answer 1

`2-e`

Explanation:

Find `f'(1)`.

To find `f'(x)`, the most important thing to know is that the derivative of `e^x` is still `e^x`.

Since the derivative of `2x` is just `2`,

`f'(x)=-e^x+2`

To find the slope (of the tangent line) at that point, plug in `1`.

`f(1)=-e^1+2=2-eapprox-0.7183`