Question

What is the absolute maximum value of f(x)=(1+x^4)e^-3x define on [0, -INF]

Answer 1

Here is my work so far. I'm having trouble find the critical values.

Answer 2

that equation doesn't have any real roots.
so no critical points.

Answer 3

*no global max or min values
hence to get absolute max or min, you put endpoints.

Answer 4

put x=0 and find f(0)
then put x= infinity and find f(infinity)
whichever is greater is your ABSOLUTE maxima

Answer 5

Oops, sorry but i typed in the question wrong...it's asking for absolute MINIMUM. But so far i got f(0)=1 and f(infinity)=0, so i'm thinking that x=0 is the minimum, but the answer key says that the minimum is not attained. Could you please explain it to me?

Answer 6

oh, sorry, end-point was -infinity
so u need to find f(-infinity) which gives you infinity
so it goes from 1(at t=0) to infinity (at t=-infinity)
then i think minimum should be at x=0...hmm

Answer 7

I think i can piece it together now! thanks for your help!:D

Answer 8

hmm..welcome ^_^