Q. 153.7( 48 Votes )

Let I be any interval disjoint from [–1, 1]. Prove that the function f given by is strictly increasing on 1.

Answer :

It is given that


Now, f’(x) =0



The points x =1 and x = -1 divide the real line in three disjoint intervals


(-∞,-1),(-1,1) and (1,∞)


Now in interval, (-1,1)


it is clear that -1 < x < 1


x2 < 1




Therefore, f’(x) = 1- < 0 (-1,1) ~ {0}


Therefore, f is strictly decreasing on (-1,1) ~ {0}


x < -1 or 1 < x


x2 > 1




Therefore, f’(x) = 1- > 0 (-∞, -1) and (1,∞)


Therefore, f is strictly increasing in interval I disjoint from (-1,1)


Hence Proved.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
How to find Maxima & Minima?How to find Maxima & Minima?How to find Maxima & Minima?43 mins
Practise Questions - Application of DerivativesPractise Questions - Application of DerivativesPractise Questions - Application of Derivatives45 mins
Interactive quizz on tangent and normal, maxima and minimaInteractive quizz on tangent and normal, maxima and minimaInteractive quizz on tangent and normal, maxima and minima43 mins
Interactive quiz on maxima and minimaInteractive quiz on maxima and minimaInteractive quiz on maxima and minima48 mins
Tangents & Normals (Concept Builder Class)Tangents & Normals (Concept Builder Class)Tangents & Normals (Concept Builder Class)55 mins
Test your knowledge of Tangents & Normals (Quiz)Test your knowledge of Tangents & Normals (Quiz)Test your knowledge of Tangents & Normals (Quiz)52 mins
Tangent & Normal To A CurveTangent & Normal To A CurveTangent & Normal To A Curve53 mins
Application of BiotechnologyApplication of BiotechnologyApplication of Biotechnology48 mins
Application of Biotechnology | Concepts - 02Application of Biotechnology | Concepts - 02Application of Biotechnology | Concepts - 0256 mins
Application of Biotechnology | Concepts - 01Application of Biotechnology | Concepts - 01Application of Biotechnology | Concepts - 0160 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