Most Important Selected Qs for JEE AdvancedMathematicsApplication of Derivatives

Let f(x)=a₁ x+a₂ 2 x+ +a_n n x , where a₁ R and n N . If |f(x)| | x| x , then the maximum value of |a₁+2 a₂+ +n a_n | is

Correct answer

Step-by-step solution

aligned & |a₁ x+a₂ 2 x+ +a_n n x | | x| & Let f(x)=a₁ x+a₂ 2 x+ +a_n x & Given |f(x)| | x|, f(0)=0 aligned aligned & f(x)= _ h 0 f(x+h)-f(x) h f(0)= _ h 0 f(h) h & also | f(h) h | | h h | |f(0)| 1 & |a₁+2 a₂+ +n a₀ | 1 aligned

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