IIT-JEE 2008 · Paper 2 · Mathematics Q16

MathematicsSingle correct+4 / -1Question 16 of 66

Passage

Paragraph for Question Nos. 14 to 16

Consider the function $f:(-\infty,\infty)\to(-\infty,\infty)$ defined by
$f(x)=\frac{x^2-ax+1}{x^2+ax+1},\quad0<a<2.$

Let
$g(x)=\int_0^{e^x}\frac{f'(t)}{1+t^2}dt.$
Which of the following is true?

g'(x)

is positive on

(-\infty,0)

and negative on

(0,\infty)

g'(x)

is negative on

(-\infty,0)

and positive on

(0,\infty)

g'(x)

changes sign on both

(-\infty,0)

and

(0,\infty)

g'(x)

does not change sign on

(-\infty,\infty)

Answer and worked solution

Official answer: B

Derivative. $g'(x)=\dfrac{f'(e^x)}{1+e^{2x}}e^x$ , with the same sign as $f'(e^x)$ .

(B)

Topics:Leibniz rule Monotonicity

IIT-JEE 2008 · Paper 2, Mathematics question 16