gabycc12 3 years ago find the critical numbers and the open intervals on which the function is increasing or decreasing. y=3x^3+12x^2+15x

1. myininaya

To find critical numbers for a polynomial you need to find f'(x) And set f'(x)=0 And solve for x These solutions to f'(x) will be your critical numbers

2. ParthKohli

lol. It took me time to realize that "critical numbers" just means "critical points". :P

3. myininaya

Do you know how to find y'?

4. gabycc12

f'(x)= 9x^2+24x+5 correct??

5. myininaya

close

6. myininaya

(15x)'=15

7. gabycc12

oh okay now what do i do after this ? f'(x)= 9x^2+24x+15

8. myininaya

Please refer to my instructions. Set f'(x)=0 and solve for x :)

9. gabycc12

i cant seem to be able to solve for x i got 3x(3x+8)=15

10. myininaya

11. gabycc12

yeah i did that and i got 8 and -8 ; but the answers in the book are -1 and -5/3

12. myininaya

So you have 9x^2+24x+15=0 correct?

13. myininaya

You could divide both sides by 3 since each term has a common factor 3 Giving you 3x^2+8x+5=0 Now you can do the quadratic formula but this is also pretty easy to factor

14. myininaya

$ax^2+bx+c=0 => x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$ Did you use this formula?

15. gabycc12

yes i did

16. myininaya

Then you need to try again, because 8 and -8 is not what you should get.

17. myininaya

What is a=? What is b=? What is c=?

18. gabycc12

a=9 b=24 c=15 correct??

19. myininaya

Sure are you could have used the equation I provided you So let's plug these numbers in that you have

20. myininaya

$x=\frac{-24 \pm \sqrt{24^2-4(9)(15)}}{2(9)}$

21. myininaya

Use order of operations to evaluate what is inside the radical

22. gabycc12

ohhh okay i see what i did wrong i multiplied -24 by 6 instead of adding and subtracting. Thank you so much for your help!