Posted by **Larry** on Thursday, October 11, 2012 at 12:28am.

If f(x)=ax^2+b

f(-3)=-3 and f'(-3)=2

find the coefficients a and b.

- Math -
**Reiny**, Thursday, October 11, 2012 at 8:49am
f(x) = ax^2 + b

f ' (x) = 2ax

given :

f ' (-3) = 2 ----> 2a(-3) = 2

-3a = 1

a = -1/3 , so f(x) = (-1/3)x^2 + b

f(-3) = -3

---> (-1/3)(-3)^2 + b = -3

-3 + b = -3

b = 0

**so a = -1/3, b = 0 and f(x) = (-1/3)x^2**

check:

f(-3) = -(1/3)(9) = -3

f ' (x) = -(2/3)x

f '(-3) = -(2/3)(-3) = 2

all looks good.

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