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NDA 2019

Exam: NDA
Year: 2019
Subject: Mathematics
Chapter: Application of Derivatives

NDA 2019 · Mathematics · Application of Derivatives

Paragraph: Consider the function f(x)=3 x^4-20 x^3-12 x^2+288 x+1...

Paragraph: Consider the function

f(x)=3 x^4-20 x^3-12 x^2+288 x+1

Question: In which one of the following intervals is the function increasing?

Options

A $(-2,3)$
B $(3,4)$
C $(-3,-2)$
D $(-4,-3)$

Correct answer

A. $(-2,3)$

Step-by-step solution

f(x)=3 x^4-20 x^3-12 x^2+288 x+1\therefore f^{\prime}(x)=12 x^3-60 x^2-24 x+288

\begin{aligned} & \Rightarrow f^{\prime}(x)=(x+2)\left(x^{\prime}-3\right)(x-4) \\ & f^{\prime}(x) > 0 \\ & \Rightarrow(x+2)(x-3)(x-4) > 0\end{aligned}

$

<br/>

\therefore \quad x \in(-2,3) \cup(4, \infty)$

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