Continuity and Differentiability: JEE Mains 2022 June 29 Shift 2

Hard· Mean value theorems· +4 / 0
Let ff and gg be twice differentiable even functions on (−2,2)(-2,2) such that f(14)=0f\left(\dfrac14\right)=0, f(12)=0f\left(\dfrac12\right)=0, f(1)=1f(1)=1 and g(34)=0g\left(\dfrac34\right)=0, g(1)=2g(1)=2. Then, the minimum number of solutions of f(x)g′′(x)+f′(x)g′(x)=0f(x)g''(x)+f'(x)g'(x)=0 in (−2,2)(-2,2) is equal to ______.
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