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Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 1 subquestion xiii maths textbook solution

Answers (1)


\text { Increasing interval }(-\infty,-2) \cup(2, \infty) \\ \text { Decreasing interval (-2,2) }


Here given that


To find:

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


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


We have,


Differentiating w.r.t. x, we get,

\begin{aligned} &f^{\prime}(x)=\frac{d}{d x}\left(2 x^{3}-24 x+107\right) \\ &\Rightarrow f^{\prime}(x)=6 x^{2}-24 \end{aligned}

For critical points we must have,

\begin{aligned} &f^{\prime}(x)=0\\ &\Rightarrow 6 x^{2}-24=0\\ &\Rightarrow 6\left(x^{2}-4\right)=0\\ &\Rightarrow x^{2}-4=0\{\therefore 6>0\}\\ &\Rightarrow x^{2}=4\\ &\Rightarrow x=\pm 2\\ &\Rightarrow x=+2,-2\\ &\text { Clearly, } f^{\prime}(x)>0 \text { if } x<-2 \text { and } x>2 \text { or } x \in(-\infty,-2) \text { and } x \in(2, \infty) \text { and } f^{\prime}(x)<0 \text { if }\\ &-2<x<2 \text { or } x \in(-2,2) \end{aligned}

\text { So, } f(x) \text { is increasing on the interval }(-\infty,-2) \cup(2, \infty) \text { and } \\ f(x) \text { is decreasing on interval (-2,2). }

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Gurleen Kaur

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