Q. 1 B5.0( 1 Vote )

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

f(x) = x2 + 2x – 5

Answer :

Given:- Function f(x) = x2 + 2x – 5


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,


f(x) = x2 + 2x – 5



f’(x) = 2x + 2


For f(x) to be increasing, we must have


f’(x) > 0


2x + 2 > 0


2x < –2



x < –1


x (–,–1)


Thus f(x) is increasing on interval (–,–1)


Again, For f(x) to be increasing, we must have


f’(x) < 0


2x + 2 < 0


2x > –2



x> –1


x (–1,∞)


Thus f(x) is decreasing on interval x (–1, ∞)


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Rapid Quiz challenge - Cell Structure & Cell DivisionRapid Quiz challenge - Cell Structure & Cell DivisionRapid Quiz challenge - Cell Structure & Cell Division52 mins
Different kind of mappingsDifferent kind of mappingsDifferent kind of mappings58 mins
Functions - 01Functions - 01Functions - 0152 mins
Functions - 10Functions - 10Functions - 1047 mins
Functions - 05Functions - 05Functions - 0558 mins
Functions - 07Functions - 07Functions - 0748 mins
Functions - 02Functions - 02Functions - 0253 mins
Functions - 03Functions - 03Functions - 0361 mins
Functions - 08Functions - 08Functions - 0840 mins
Functions - 12Functions - 12Functions - 1252 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses