Given
f''(x)=5x−6
and f'(−3)=−6 and f(−3)=2.
find f'(x) and f(1)
f'' = 5x-6
f' = 5/2 x^2 - 6x + C
f'(-3) = -6 so,
-6 = 5/2 (9) - 6(-3) + C
C = -93/2
f'(x) = 5/2 x^2 - 6x - 93/2
f(x) = 5/6 x^3 - 3x^2 - 93/2 x + C
f(-3) = 2 so
2 = 5/6 (8) - 3(4) - 93/2 (-3) + C
C = -793/6
f(x) = 5/6 x^3 - 3x^2 - 93/2 x - 793/6
f(1) = 5/6 - 3 - 93/2 - 793/6 = -1085/6