Let y=P(x) be a differentiable function x [0, ) such that d d x (P(x))+(x-1)^3 P(x)+1 x [0, ) . If P(x) x^3+3 x+1 x [0, ) and P(0)=1 then which of the following is/are correct?

Question

Quantrex Academy · Accepted Answer

Correct answer: B. Area bounded by y=P(x) ; x -axis; x=0 and x=1 is 11 4

d d x (P(x))+(x-1)^3-(P(x)+1) 0 e^ -x ( d P(x) d x -P(x)+x^3-3 x^2+3 x-2 ) 0 aligned & d d x (P(x) e^ -x )- d d x e^ -x x^3-3 d d x x e^ -x - d d x e^ -x 0 & d d x (P(x)- (x^3+3 x+1 ) ) e^ -x 0 aligned Let g(x)= (P(x)- (x^3+3 x+1 ) ) e^ -x is increasing g(x) g(0) (P(x)- (x^3+3 x+1 ) ) e^ -x 0 x 0 array ll but & P(x) x^3+3 x+1 x 0 & P(x)=x^3+3 x+1 x 0 array

Let y=P(x) be a differentiable function x [0, ) such that d d x (P(x))+(x-1)^3 P(x)+1 x [0, ) . If P(x) x^3+3 x+1 x [0, ) and P(0)=1 then which of the following is/are correct?

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Correct answer

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