Thread: Use the first derivative test to identify all relative extrema

Find the intervals on which the function f(x) = (x^2 + 4x + 4)(x - 1) is increasing or decreasing. Apply the first derivative test to identify all relative extrema.

Thank you.

Hi,

This is a very standard Calculus problem so I think you should show an attempt at the problem before getting help. You should know from class how to find the critical points. Show some effort and if you're still stuck we'll help you out.

ok,

f(x) = (x^2 + 4x + 4)(x-1)
f '(x) = 3x^2 + 6x
3x(x+2) = 0

x= -2
x= 0
ok so i got this far what do i do to find the relative extrema?

Good work! That's perfect so far. Now I find the best way to test for critical points is to draw a number line and mark the two points you found. Those points mark a slope of 0, or similarly at those points f'(x)=0. So the regions inbetween these points there will be a consistent positive or negative slope. Use test points inbetween your critical points to determine the slope for that region. If the slope changes from positive to negative or from negative to positive before and after a critical point, you then have a relative extrema.

Alright, thank you