Find the inflection point of the function: f(x) = xe^-2x

Question

anonymous · Answer

$$f''(x)= -4e ^{-2x}(1-1x)$$

I got this by finding the second derivative. 

So I know the inflection points are where f(x)=0 and f(1) should be one of these points, but in the book they give the answer as $$(1, e ^{-2})$$

anonymous · Answer

Can someone explain where the e^-2 comes from.

anonymous · Answer

@SolomonZelman

freckles · Answer

assuming you found the correct second derivative
you find when f'' equals 0
which is when 1-x=0 
x=1
plug in 1 into f
f(1)=1*e^(-2*1)

freckles · Answer

the original function tells you where x occurs
the derivative functions tell you the slope at x
the derivative of the derivative function tells you the concavity at x

freckles · Answer

we want to know where we have an inflection point

freckles · Answer

you found the x at which it occurs

freckles · Answer

but to find where that x occurs (as in finding the corresponding y value)
you need to use the original function

anonymous · Answer

Ahhh @freckles thats right. Thanks :)