Get Answers to all your Questions

header-bg qa

Explain solution RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 1 subquestion iv maths

Answers (1)


\text {Increasing interval}(-\infty, 1) \cup(3, \infty) \\ \text {Decreasing interval}(1,3)


Here given that


To find:

We have to find out the intervals in which function is increasing and decreasing.


Firstly we will find critical points and then use increasing and decreasing property.


Given that


On differentiating we get,

\begin{aligned} &f^{\prime}(x)=\frac{d}{d x}\left(2 x^{3}-12 x^{2}+18 x+15\right) \\ &\Rightarrow f^{\prime}(x)=6 x^{2}-24 x+18 \end{aligned}

Firstly we will find critical points for f(x).

For this we have,

\begin{aligned} &f^{\prime}(x)=0 \\ &\Rightarrow 6 x^{2}-24 x+18=0 \\ &\Rightarrow 6\left(x^{2}-4 x+3\right)=0 \\ &\Rightarrow x^{2}-3 x-x+3=0\{\therefore 6>0\} \\ &\Rightarrow(x-3)(x-1)=0 \\ &\Rightarrow x-3=0 \text { and } x-1=0 \\ &\Rightarrow x=3 \text { and } x=1 \end{aligned}

\begin{aligned} &\text { Clearly, } f^{\prime}(x)>0, f(x)<1 \text { and } x>3 \text { or } x \in(-\infty, 1) \text { and } x \in(3, \infty) \text { and } f^{\prime}(x)<0 \text { if }\\ &1<x<3 \text { or } x \in(1,3) \end{aligned}

\text { So, } f(x) \text { is increasing the interval }(-\infty, 1) \cup(3, \infty) \text { and } f(x) \text { is decreasing on interval }(1,3) \text { . }

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support