RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 27 of Exercise 17.2

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27

Find the intervals in which f(x) = (x + 2)e–x is increasing or decreasing ?

we have,

f(x) = (x + 2)e–x


f'(x) = e–x – e–x (x+2)


= e–x (1 – x – 2)


= – e–x (x+1)


Critical points


f'(x) = 0


– e–x (x + 1) = 0


x = – 1


Clearly



Hence f(x) increases in (–,–1), decreases in (–1, ∞)


Chapter Exercises

More Exercise Questions

26

Find the interval in which is increasing or decreasing ?