Find what f(x) is using the following:

Question

Suppose f"(x) = -24x - 14, f'(-1)=12, and f(-1)= -21.

Answer 1

f"(x) -24x - 14

f'(x) = -12x^2 -14x + c

f'(-1) = 12 = -12+14 + c = c+2

c = 12-2 = 10

f'(x) = -12x^2 -14x + 10

f(x) = -4x^3 -7x^2 +10x + k

f(-1) =-21 = 4-7-10+k

k =-21 + 13 = -8

f(x) = -4x^3 -7x^2 +10x -8