Question

What are all values of x for which the function
f defined by f(x) = (x^2 −3)e^−x is increasing?
A. All values of x
B. −3 < x < 1
C. x < −1 and x > 3
D. There are no such values of x
E. −1 < x < 3

Answer 1

A function is increasing where its derivative is positive.

So find where f ' (x) > 0.

Answer 2

Is this a calculus or pre calculus question?

For calculus you need derivatives. For precalc, use a calculator.

Answer 3

Find the derivative of the function and find out there the slope is greater than and the zeros of the original function and from there you should be able to get it.
Answer is E