2007-09-12 01:16:38 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
a = - 4 and c = 1 worked out as under:
f ( - 3/2 ) = 10
=> a ( - 3/2 )^2 - 12 ( - 3/2 ) + c = 10
= (9/4) a + 8+ c = 0 ... ( 1 )
For maximum value of f ( x ),
f' ( x ) = 2ax - 12 = 0
=> x = 6/a = - 3/2
=> a = - 4
Putting this value of a = - 4 in eqn. ( 1 ), c = 1
2007-09-12 01:32:46 · answer #1 · answered by Madhukar 7 · 0⤊ 0⤋
f'(x) = 2ax - 12. f'(x) = 0 at x = 6/a which is -3/2, so a = -4. Now we know that f(x) = -4x^2 - 12x + c; since f(-3/2) = 10, we find c = 1, so f(x) = -4x^2 - 12x + 1.
2007-09-12 01:33:02 · answer #2 · answered by Tony 7 · 0⤊ 0⤋
f'(x) = 2ax-12.
2a*(-3/2)-12=0.
a(-3/2) = 12/2=6.
a=6(-2/3) = -4.
f(-3/2)=-4(-3/2)^2- 12(-3/2)+c=10.
So, -9+18+c=10.
So, c=10-9=1.
I think.
2007-09-12 01:36:19 · answer #3 · answered by yljacktt 5 · 0⤊ 0⤋