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Functions question

2010 · Shift 2 · Q36

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PYQ Library
JEE Advanced
Mathematics
Functions
2010 · Shift 2 · Q36

Functions question

2010 · Shift 2 · Q36

JEE AdvancedMathematicsFunctionsMCQ+4 / −1

Consider the polynomial

f\left( x \right) = 1 + 2x + 3{x^2} + 4{x^3}.

Let

s

be the sum of all distinct real roots of

f(x)

and let

t = \left| s \right|.

The function

f'(x)

is

A
increasing in $\left( { - t, - {1 \over 4}} \right)$ and decreasing in $\left( { - {1 \over 4},t} \right)$
B
decreasing in $\left( { - t, - {1 \over 4}} \right)$ and increasing in $\left( { - {1 \over 4},t} \right)$
C
increasing in $(-t, t)$
D
decreasing in $(-t, t)$

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