JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f\) and \(g\) be twice differentiable even functions on \((-2,2)\) such that \(f\left(\frac{1}{4}\right)=0, f\left(\frac{1}{2}\right)=0, f(1)=1\) and \(g\left(\frac{3}{4}\right)=0, g(1)=2\) Then, the minimum number of solutions of \(f(x) g^{\prime \prime}(x)+f^{\prime}(x) g^{\prime}(x)=0\) in \((-2,2)\) is equal to
- A \(0\)
- B \(2\)
- C \(4\)
- D \(6\)
Answer & Solution
Correct Answer
(C) \(4\)
Step-by-step Solution
Detailed explanation
Let \(h(x)=f(x) g^{\prime}(x) \rightarrow 5\) roots \(\because f ( x )\) is even \(\Rightarrow\) \(f \left(\frac{1}{4}\right)= f \left(\frac{1}{2}\right)= f \left(-\frac{1}{2}\right)= f \left(\frac{1}{4}\right)=0\) \(g ( x )\) is even…
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