JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

f(x)

is a non-zero polynomial of degree four, having local extreme points at

x = - 1,\,0,\,1,

then the set

S = \left\{ {x \in R:f(x) = f(0)} \right\}

contains exactly

View answer and explanation

Correct option: D

two irrational and one rational number

The correct answer is D (two irrational and one rational number) because the polynomial equation

f(x) = f(0)

has solutions

x = 0, \pm \sqrt{2}

, resulting in one rational and two irrational roots.

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f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

x

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a

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\sin x-\cos x-a x+b

f(x)=x e^{x(1-x)}, x \in R

f

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fog

f\left( x \right) = {x^3} + b{x^2} + cx + d

0 < {b^2} < c

\left( { - \infty ,\;\infty } \right)