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

Jan 6, 2016

$2 - e$

#### Explanation:

Find $f ' \left(1\right)$.

To find $f ' \left(x\right)$, the most important thing to know is that the derivative of ${e}^{x}$ is still ${e}^{x}$.

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

$f ' \left(x\right) = - {e}^{x} + 2$

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

$f \left(1\right) = - {e}^{1} + 2 = 2 - e \approx - 0.7183$