Applications of differentiation

[abby_07]

I dont know if i am doing this right
What i have to do is find the critical numbers of f ( if any), find the open interval on which the algerbraic function is increasing or decreasing, and locate all relative extrema.

f(x)=(x-1)^2 (x+2)
f'(x)=3x^2-3
criticle numbers are -1 and 1
after that i do not no what to do

can you please help
abby

 

[des4ij]

hint

try plugging in numbers before -1, between -1 and 1, and after 1... the sign on the value u get will tell u something about the slope...

 

[galactus]

You found your critcal values, -1 and 1.

Draw a graph. They help. Check values on both sides of your critical points. If it's < 0, then the slope is decreasing. If it's > 0, then the slope is increasing.

YOu can look at the graph and tell whether it's increasing, decreasing, concave up, concave down, etc.

Also, check your 2nd derivative. Check -1 and 1. If f''(x) > 0, then minimum. If f''(x) < 0, then maximum.

If f''(x) > 0 on an open interval, then concave up.

If f''(x) < 0 on an open interval, then concave down.

 

[abby_07]

so is (- infinity, -1) decreasing and (1, positive infinity) increasing

i still dont understand how to find the max an min etrema