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For x , t in R let p(t) (x)= ( sin...

For ` x , t in R ` let
` p_(t) (x)= ( sin t) x^(2) - (2 cost ) x + sin t` be a family of quadratic polynomials in x with variable coefficients. Let `A(t) = int_(0)^(1) p_(t) ( x)dx ` , Which of the following statements are true?
(I) `A(t) lt 0 `for all t.
(II) A(t) has infinitely many critical points.
(III) A(t) = 0 for infinitely many t.
(IV) `A'(t) lt 0` for all t.

A

(I) and (II) only

B

(II) and (III) only

C

(III) and (IV) only

D

(IV) and (I) only

Text Solution

Verified by Experts

The correct Answer is:
B
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