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