Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Let f:[0, ) R be a continuous strictly increasing function such that f^3(x)= ₀^x t f^2(t) d t x 0 then value of f(6) is

Correct answer

Step-by-step solution

f^3(x)= ₀^x t f^2(t) d t ....(1) Differentiate with respect to x3 f^2(x) f^ (x)=x f^2(x) f^ (x)= x 3 f(x)= x^2 6 +C ....(2) But from (1) f^3(0)=0 f(0)=0 From (2) C=0 f(x)= x^2 6 f(6)= 6^2 6 =6

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