JEE Mains · Maths · STD 12 - 5. continuity and differentiation
If \(f(x)=x^2+g^{\prime}(1) x+g^{\prime \prime}(2)\) and \(g(x)=f(1) x^2+x f^{\prime}(x)+f^{\prime \prime}(x),\) then the value of \(f(4)-g(4)\) is equal to \(...........\).
- A \(13\)
- B \(12\)
- C \(14\)
- D \(11\)
Answer & Solution
Correct Answer
(C) \(14\)
Step-by-step Solution
Detailed explanation
\(f(x)=x^2+g^{\prime}(1) x+g^{\prime \prime}(2)\) \(f^{\prime}(x)=2 x+g^{\prime}(1)\) \(f^{\prime \prime}(x)=2\) \(g(x)=f(1) x^2+x\left[2 x+g^{\prime}(1)\right]+2\) \(g^{\prime}(x)=2 f(1) x+4 x+g^{\prime}(1)\) \(g^{\prime \prime}(x)=2 f(1)+4\) \(g^{\prime \prime}(x)=0\)…
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