Given the function f(x) = ax^3 + bx^2 + 3x - 2,

and f(2) = 10 and f ' (-1) = 14,
solve for A and B.

1 answer

f(x) = ax^3 + bx^2 + 3x - 2
f'(x) = 3ax^2 + 2bx + 3
f'(-1) = 3a - 2b + 3 = 14
3a - 2b = 11 **

also f(2) = 10
8a + 4b + 6 - 2 = 10
8a + 4b = 6
4a + 2b = 3 ***

add ** and ***
7a = 14
a = 2 , put that back into ** to find b