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

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Answer 1 · 2016-01-06T02:45:16

$2-e$

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 $1$ .

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

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