## burhan101 2 years ago Determine the derivative, all the critical numbers and the intervals of increase and decrease y=-5x²+20x+2

1. burhan101

$\huge y'=-10x+20$ $\huge 0=-10x+20$ $x=2$

2. burhan101

i get : intervals of increase x<2 intervals of decrease x>2 but the answer key says the opposite

3. Abhishek619

when $y \prime >0,$ then increasing.

4. burhan101

what's in intervals of increase / decrease tho?

5. koymoi

I got the same answer as you @burhan101 intervals of increase x<2 intervals of decrease x>2

6. Abhishek619

x>2 it decreases x<2 it increases.

7. johnweldon1993

Right...I as well @koymoi ...I think maybe your answer key is wrong @burhan101

8. burhan101

think the answer key's wrong then ?

9. dan815

yes

10. burhan101

yeah, i thought it was a fairly straight forward question

11. dan815

graph it and ull know for sure

12. dan815

|dw:1371791477746:dw|

13. xartaan

14. dan815

|dw:1371791538467:dw|

15. dan815

oh oops that shud be + when i multiplied by -5

16. dan815

|dw:1371791697708:dw|

17. dan815

+22

18. dan815

|dw:1371791721412:dw|

19. genius12

@burhan101 u don't need calculus to find intervals of increase/decrease. This is a parabola with a negative leading coefficient so it opens down. Using -b/2a we get -b/2a = 2, which is the x-coordinate of the vertex of the parabola. Since it opens down, function is increasing on $$\bf (-\infty,2)$$ and decreasing on $$\bf (2,\infty)$$