# Thread: increasing and decreasing functions

1. ## increasing and decreasing functions

ok here is the problem, consider a function f whose derivative is given by f'(x) = (x-4)^2 * e^(-x/2).

a.) the function f is increasing on the interval?

b.) the function f is concave up on the interval(s)

c.) the function f is concave down on the interval(s)

ok so what i dont get is how to find the critical points. i only see one in the problem and thats 4.? right? and to find the concave up or down i would apply the second derivative test? this problem gets really messy once i try to do the 2nd derivative test. there has to be an easier way. can anyone help me out?

2. Originally Posted by slapmaxwell1
ok here is the problem, consider a function f whose derivative is given by f'(x) = (x-4)^2 * e^(-x/2).

a.) the function f is increasing on the interval?

b.) the function f is concave up on the interval(s)

c.) the function f is concave down on the interval(s)

ok so what i dont get is how to find the critical points. i only see one in the problem and thats 4.? right?

yes, for f'(x)

and to find the concave up or down i would apply the second derivative test? this problem gets really messy once i try to do the 2nd derivative test. there has to be an easier way. can anyone help me out?

show your work for f''(x)
...

3. Originally Posted by skeeter
...
well for the 2nd derivative test, i would use the quotient rule. f"(x) = [(x-4)^2]/e^(x/2) = ok ok ok i got the critical points using the second derivative test. x = 4, 8 well the critical points for the function are 4 and 8. now i have to test them to see where the concave up and down is.

4. ok wait lets go back to the original problem, the answer in the back of the book says the answer is (-infinity, infinity) this is where the function is increasing?

5. Originally Posted by slapmaxwell1
ok wait lets go back to the original problem, the answer in the back of the book says the answer is (-infinity, infinity) this is where the function is increasing?
yes ... $(x-4)^2 \cdot e^{-x/2} \ge 0$ for all x