can someone help me out? i

Question

For the function f(x) = ax^3 + bx^2 -5x + 9

determine the values of a and b so that

f(-1) = 12 and f ' (-1) = 3

Answer 1

f(x) = ax³ + bx² - 5x + 9

f'(x) = 3ax² + 2bx - 5

Since f(-1) = 12, -a + b + 14 = 12

Since f'(-1) = 3, 3a - 2b - 5 = 3

So, we have the system of equations:

-a + b = -2

3a - 2b = 8

Multiply the first equation by 2:

-2a + 2b = -4

3a - 2b = 8

Add the equations to get a = 4.

a = 4 and b = 2