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Please solve RD Sharma class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 1 subquestion xvii 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 f(x) is increasing or decreasing.


First 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+7\right) \\ &\Rightarrow f^{\prime}(x)=6 x^{2}-24 \end{aligned}

For f(x) we have to find critical points,

We must have,

\begin{aligned} &f^{\prime}(x)=0\\ &\Rightarrow 6 x^{2}-24=0\\ &\Rightarrow 6 x^{2}=24\\ &\Rightarrow x^{2}=\frac{24}{6}\\ &\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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