Let f(x) = x*e^-x^2
Let F'(x) = e^-x^2 (1-2x^2)
Determine intervals where the function is increasing and intervals where the function is decreasing, and the local extrema (if any).

Question

Let f(x) = x*e^-x^2
Let F'(x) = e^-x^2 (1-2x^2)
Determine intervals where the function is increasing and intervals where the function is decreasing, and the local extrema (if any).

idku · Answer

to determine where the f(x) is increasing. Set f'(x) equal to zero.
Then, for x values that f'(x) is greater than zero, this is where the f(x) is increasing.

idku · Answer

and it would be DEcreasing where f'(x) is less than zero.

idku · Answer

and the derivative you got, is correct.

idku · Answer

questions?

anonymous · Answer

so to find the values of x I would set it up as 0 = 1-2x^2 which gives sqrt(1/2) and 0 = e^-x^2 which gives no solution. Which would mean that my intervals would be at -1/2, 0 and 1/2. Is that correct?

anonymous · Answer

@idku

idku · Answer

(1-2x^2) is negative for any x values, besides
x=0
and when
(absolute value of x )<sqrt{2}/2

idku · Answer

the why and the rest is yours.