Question

What are all values of x for which the function f defined by f(x) = (x^2 - 3)e^-x is increasing?

Answer 1

Answers are:
a. There are no such values of x
b. x<1 and x>3
c. -3<x<3
d. -1<x<3
e. All values of x

Answer 2

your job is to solve
\[f'(x)>0\]

Answer 3

\[f'(x)=e^{-x}(-x^2+2 x+3)\] and we can ignore the
\[e^{-x}\]part because that is always positive

Answer 4

so really you have to solve
\[-x^2+2x+3>0\]

Answer 5

zeros are at -1 and 3, so answer is
\[-1<x<3\]

Answer 6

You're the best thanks!