A. Find the critical numbers
B. the largest open intervals where the function is increasing
C. the largest open intervals where it is decreasing

f(x)= 2/3x^3 - x^2 - 4x + 2

Question

A. Find the critical numbers
B. the largest open intervals where the function is increasing 
C. the largest open intervals where it is decreasing 

f(x)= 2/3x^3 - x^2 - 4x + 2

anonymous · Answer

is it 
$$f(x)=\frac{2}{3}x^3-x^2-4x+2$$?

credmond · Answer

Yep!

anonymous · Answer

k
did you take the derivative?

credmond · Answer

No, I didn't really know where to start :/

anonymous · Answer

take the derivatives using the power rule

anonymous · Answer

clear or no?

credmond · Answer

Yeah so the derivative would be 
2x^2- 2x -4 
right?

anonymous · Answer

right
now set it equal to zero and solve

anonymous · Answer

you got that part? this problem has been cooked up, so the derivative factors easily

credmond · Answer

so I got x = 2, and -2 right

anonymous · Answer

no

credmond · Answer

oh wait... 
2 and -1

anonymous · Answer

$$2x^2- 2x -4 =2(x^2-x-2)=2(x+1)(x-2)$$ 
$$(x+1)(x-2)=0$$ so ... yeah, those

credmond · Answer

haha okay!

anonymous · Answer

ok the critical numbers at $-1$ and $2$

anonymous · Answer

you don't really need anything else to finish the problem
you know the two critical numbers, and you know that a cubic polynomial with positive leading coefficient looks something like ths
|dw:1393131804430:dw|

anonymous · Answer

i.e. it is increasing, then decreasing, then increasing
you could also check the sign of the derivative on the open intervals $(-\infty, -1),(-1,2),(2,\infty)$ to see where it is positive and where it is negative
you good from there, or you need more help?

credmond · Answer

Okay, cool. I think I'm good from here!

anonymous · Answer

k
good luck

credmond · Answer

Thank you so much for the help! I really appreciate it! :)

anonymous · Answer

yw