Range of polynomial P(x)=4 x^3-3 x as x varies over interval left(-frac{1}{2}, frac{1}{2}right) is

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1.Relation and Function

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The range of the polynomial $P(x)=4 x^3-3 x$ as $x$ varies over the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is

A

$[-1,1]$

B

$(-1,1]$

C

$(-1,1)$

D

$\left(-\frac{1}{2}, \frac{1}{2}\right)$

(KVPY-2016)

Solution

(c)

We have,

$P(x)=4 x^3-3 x x \in\left(-\frac{1}{2}, \frac{1}{2}\right)$

$P^{\prime}(x)=12 x^2-3=3\left(4 x^2-1\right)$

$P^{\prime}(x)<0 x \in\left(-\frac{1}{2}, \frac{1}{2}\right)$

Standard 12

Mathematics

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