Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

If the function f(x)=2 x^3-9 a x^2+12 a^2 x+1 has a local maximum at x=x₁ and a local minimum at x=x₂ such that x₂=x₁^2 , then a is equal to

Correct answer

Step-by-step solution

f^ (x)=6 x^2-18 a x+12 a^2=0 x=a, 2 a Given x₂=x₁^2 , so a cannot be negative. If a 0 , then local minimum occurs at x=2 a and local maximum at x=a . Thus x₁=a and x₂=2 a 2 a = a ^2 a =2 (if a =0, f ( x ) is always increasing)

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