Given that \(f '(x) = 3x^{2} - 6x + 1\) and f(3) = 5, find
FURTHER MATHEMATICS
WAEC 2008
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: C. \(f(x) = x^{3} - 3x^{2} + x + 2\)
Explanation
\(f ' (x) = 3x^{2} - 6x + 1\)
\(f(x) = \int (3x^{2} - 6x + 1) \mathrm {d} x\)
= \(x^{3} - 3x^{2} + x + c\)
\(f(3) = 5 = 3^{3} - 3(3^{2}) + 3 + c\)
\(27 - 27 + 3 + c = 5 \implies 3 + c = 5\)
\(c = 2\)
\(f(x) = x^{3} - 3x^{2} + x + 2\)
Post an Explanation Or Report an Error
If you see any wrong question or answer, please leave a comment below and we'll take a look. If you doubt why the selected answer is correct or need additional more details? Please drop a comment or Contact us directly. Your email address will not be published. Required fields are marked *