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JEE Advanced Mathematics question

MathematicsApplication of DerivativesJEE Advanced

Let for all real values of . Then

Answer: (A),(C)

Solution

h'(x) = f'(x) - 2f(x)f'(x) + 3\{f(x)\}^2 f'(x) = [1 - 2f(x) + 3\{f(x)\}^2]f'(x).

Complete the square:

- 2f + 1 = - Missing argument for \tfrac\tfrac23 f + Missing argument for \tfrac\tfrac19) + Missing argument for \tfrac\tfrac23 = 3(f - Missing argument for \tfrac\tfrac + Missing argument for \tfrac\tfrac23 > 0 .

So always has the same sign as .

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Question ID VK-109444