Given that (f ‘(x) = 3x^{2} – 6x + 1) and f(3) = 5, find f(x).
-
A.
(f(x) = x^{3} – 3x^{2} + x + 20) -
B.
(f(x) = x^{3} – 3x^{2} + x + 31) -
C.
(f(x) = x^{3} – 3x^{2} + x + 2) -
D.
(f(x) = x^{3} – 3x^{2} + x – 13)
Correct Answer: Option C
Explanation
(f ‘ (x) = 3x^{2} – 6x + 1)
(f(x) = int (3x^{2} – 6x + 1) mathrm {d} x)
= (x^{3} – 3x^{2} + x + c)
(f(3) = 5 = 3^{3} – 3(3^{2}) + 3 + c)
(27 – 27 + 3 + c = 5 implies 3 + c = 5)
(c = 2)
(f(x) = x^{3} – 3x^{2} + x + 2)