## giggles123 3 years ago let f(x)=ax^3+6x^2+bx+4. Determine the constant a and b such that f has a relative min at x=-1 and a rel max at x=2@Algebra

1. Hero

I hate these

2. moneybird

first derivative of f(x) first

3. giggles123

I did that then what? I got F'(x)=3ax^2+12x+b

4. myininaya

\[f'(x)=3a^2+12x+b\] \[f'(-1)=0 ;f'(2)=0\]

5. myininaya

\[f'(x)=3ax^2+12x+b*\]

6. Hero

I was just about to say....what happened to the x?

7. myininaya

\[f'(-1)=3a-12+b=0\]

8. myininaya

\[f'(2)=3a(4)+12(2)+b=0\]

9. myininaya

\[3a+b=12\] \[12a+b=-24\]

10. moneybird

3a + b =12 12a + 24 +b = 0 12a + b =-24 -(3a + b) = 12 9a = -36 a = -4 b =24

11. giggles123

what happened to the x?

12. myininaya

\[ 3a+b=12\] \[-(12a+b=-24)\] ------------------ -9a+0b=36 -9a=36 a=-4 -12+b=12 b=24 gj money

13. myininaya

what do you mean what happen to x?

14. giggles123

how did you go from f'(x)=3ax^2+12x+b* to f′(−1)=3a−12+b=0

15. myininaya

\[f(a)=-4x^3+6x^2+24x+4\]

16. myininaya

-1 and 2 are critical numbers this is a polynomial so our critical numbers only exist when f'=0

17. myininaya

f'(-1)=0 f'(2)=0

18. myininaya

this was given to us

19. myininaya

money and i applied these conditions to f'

20. giggles123

I got it. Thank you so much!

21. luckey

here b can take any value and a is rrestricted to any value in the interval (-2,2)