RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 1 of Exercise 17.2

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1

Find the intervals in which the following functions are increasing or decreasing.

f(x) = x8 + 6x2

Given:- Function


Theorem:- Let f be a differentiable real function defined on an open interval (a,b).


(i) If f’(x) > 0 for all , then f(x) is increasing on (a, b)


(ii) If f’(x) < 0 for all , then f(x) is decreasing on (a, b)


Algorithm:-


(i) Obtain the function and put it equal to f(x)


(ii) Find f’(x)


(iii) Put f’(x) > 0 and solve this inequation.


For the value of x obtained in (ii) f(x) is increasing and for remaining points in its domain it is decreasing.


Here we have,






For f(x) lets find critical point, we must have


f’(x) = 0





Since is a complex number, therefore only check range on 0 sides of number line.





clearly, f’(x) > 0 if x > 0


and f’(x) < 0 if x < 0


Thus, f(x) increases on (0, ∞)


and f(x) is decreasing on interval x (–∞, 0)



Chapter Exercises

More Exercise Questions

26

Find the interval in which is increasing or decreasing ?