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  • Need solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 27

Need solution for RD Sharma maths class 12 chapter Increasing and Decreasing Functions exercise 16.2 question 27

Answers (1)

Answer:

f(x) is increasing in (-\infty,-1)

and f(x) is decreasing in (-1,\infty)

Given:

f(x)=(x+2)e^{-x}

To find:

We have to find the intervals in which f(x) is increasing and decreasing.

Hint:

First, we find critical point then find property of increasing and decreasing intervals.

Solution:

we have

f(x)=(x+2)e^{-x}

Differentiating w.r.t. x we get,

\begin{aligned} &f^{\prime}(x)=e^{-x}-e^{-x}(x+2) \\ &=e^{-x}(1-x-2) \\ &=-e^{-x}(x+1) \end{aligned}

For critical points.

\begin{aligned} &f^{\prime}(x)=0 \\ &\Rightarrow-e^{-x}(x+1)=0 \\ &\Rightarrow x=-1 \\ &\text { Clearly, } f^{\prime}(x)>0 \text { if } x<-1 \\ &\text { and } f^{\prime}(x)<0 \text { if } x<-1 \end{aligned}

Hence, f(x) is increasing in (-\infty,-1), decreasing in (-1,\infty)

Posted by

Gurleen Kaur

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