If \(f(x) = 3x^{3} + 8x^{2} + 6x + k\) and \(f(2) = 1\), find the value of k.
-
-67
- -61
- 61
- 67
The correct answer is: A
Explanation
\(f(x) = 3x^{3} + 8x^{2} + 6x + k\)
\(f(2) = 3(2^{3}) + 8(2^{2}) + 6(2) + k = 1\)
\(\implies 24 + 32 + 12 + k = 1\)
\(68 + k = 1 \therefore k = 1 - 68 = -67\)