Can someone please help me out with this?

Use the First or Second Derivative test to find all relative maxima and relative minima of the funtion f(x) = e^(x^2)

I got to f'(x)=2xe^(x^2) but I'm not sure how to find the critical numbers or what to do next.

Question

Can someone please help me out with this?

Use the First or Second Derivative test to find all relative maxima and relative minima of the funtion f(x) = e^(x^2)

I got to f'(x)=2xe^(x^2) but I'm not sure how to find the critical numbers or what to do next.

perl · Answer

the critical numbers in the domain of f(x) , 
are when f ' (x) = 0 , and f ' (x) is undefined

credmond · Answer

So then what do you do next?

perl · Answer

solve f'(x)=0 
or solve
2xe^(x^2) = 0

perl · Answer

use zero product property. if A*B = 0, then A  = 0 or B = 0

credmond · Answer

So the critical number is 0?

perl · Answer

yes

perl · Answer

since e^(x^2) is never equal to zero

perl · Answer

now take the second derivative and find f ' ' (0)

credmond · Answer

is it just e^(x^2)?

perl · Answer

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