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Limits Continuity and Differentiability question

2008 · Shift 2 · Q23

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PYQ Library
JEE Advanced
Mathematics
Limits Continuity and Differentiability
2008 · Shift 2 · Q23

Limits Continuity and Differentiability question

2008 · Shift 2 · Q23

JEE AdvancedMathematicsLimits Continuity and DifferentiabilityMCQ+3 / −1

Consider the function

f:\left( { - \infty ,\infty } \right) \to \left( { - \infty ,\infty } \right)

defined by

f\left( x \right) = {{{x^2} - ax + 1} \over {{x^2} + ax + 1}},0 \lt a \lt 2.

Which of the following is true?

A
$f(x)$ is decreasing on $(-1,1)$ and has a local minimum at $x=1$
B
$f(x)$ is increasing on $(-1,1)$ and has a local minimum at $x=1$
C
$f(x)$ is increasing on $(-1,1)$ but has neither a local maximum nor a local minimum at $x=1$
D
$f(x)$ is decreasing on $(-1,1)$ but has neither a local maximum nor a local minimum at $x=1$

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