Find the smallest value of a so that the function y=e^(2x) *x^2 * a*e^(2x)+3 would be growing no matter what the x value is.

Question

Find the smallest value of a so that the function y=e^(2x)  *x^2 *  a*e^(2x)+3 would be growing no matter what the x value is.

anonymous · Answer

The answer given is 1.

anonymous · Answer

Sorry, I made a mistake. The function is y=e^(2x)  *x^2+a*e^(2x)+3

experimentx · Answer

what does "would be growing no matter what the x value is" mean??

anonymous · Answer

The function gets bigger not smaller.

experimentx · Answer

a>0

anonymous · Answer

Oh, alright. Thanks!

experimentx · Answer

seems to be growing for a=0.001

experimentx · Answer

wait thats not correct

experimentx · Answer

experimentx · Answer

I think a=1 is the right answer ...

experimentx · Answer

anonymous · Answer

But how do you get it?

experimentx · Answer

for a=0, we have  y=e^(2x) (x^2) +3 and this (x^2) is less than 1 between 0 to 1 and is decreasing the function.

experimentx · Answer

anonymous · Answer

Oh, alright.

experimentx · Answer

@ErkoT you still there ??? still I am quite incorrect

experimentx · Answer

y=e^(2x) (x^2) +3  increases between 0 to 1

it decreases on -1 to 0

experimentx · Answer

ah ... i found the best way, take derivative of e^(2x) (x^2+a)
and it must be > 0, and find the value of a as x->-0