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JEE Main202229 Jun 2022Evening ShiftMathematicsApplication of DerivativesActual

Let f and g be twice differentiable even functions on - 2 , 2 such that f 1 4 = 0 , f 1 2 = 0 , f 1 = 1 and g 3 4 = 0 , g 1 = 2 Then, the minimum number of solutions of f x g " x + f ' x g ' ' x = 0 in - 2 , 2 is equal to _____.

Correct answer

0

Step-by-step solution

Let h x = f x g ' x roots ∵   f x is even ⇒ f 1 4 = f 1 2 = f - 1 2 = f 1 4 = 0 and g x has two roots as g 3 4 = g - 3 4 = 0 (as g x is even function) So, h x = f x g ' x will have 5 roots, hence its derivative h ' x = f x g " x + f ' x g ' x will have 4 roots.

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