Question

29. Let f be the function given by ( ) 2 x f x xe− = . From the values of x given below, find a value of x so that the slope of the line tangent to the graph of f at ( xfx , ( )) is equal to 0.2?

Answer 1

tangent line:

$y-y_0=f'(x_0)(x-x_0)$

$f'(x_0)$ is slope of the tangent line at x₀

$f(x)=xe^{-2x}$

$f'(x)=-2xe^{-2x}+e^{-2x}=(1-2x)e^{-2x}$

$f'(x_0)=(1-2x_0)e^{-2x_0}=0.2$

$x_0=0.313$