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Consider the function f:(-oo,oo)rarr(-oo...

Consider the function `f:(-oo,oo)rarr(-oo,oo)` defined by `f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2`, and let `g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2)`. Which of the following is true? (A) `g\'(x)` is positive on `(-oo,0)` and negative on `(0,oo)` (B) `g\'(x)` is negative on `(-oo,0)` and positive on `(0,oo)` (C) `g\'(x)` changes sign on both `(-oo,0)` and `(0,oo)` (D) `g\'(x)` does not change sign on `(-oo,oo)`

A

g'(x) is positive on `(-oo,0)` and negative on `(0,oo)`

B

g'(x) is negative on `(-oo,0)` and positive on `(0,oo)`

C

g'(x) change sign on both `(-oo,0) and (0,oo)`

D

g'(x) does not change sign in

Text Solution

Verified by Experts

The correct Answer is:
A
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