Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • Prove that the function given by f (x) = x ^3 – 3 x ^2 + 3 x – 100 is increasing in R.

18) Prove that the function given by f (x) = x^3 - 3x^2 + 3x - 100 is increasing in R.

Answers (1)

best_answer

Given function is,
f (x) = x^3 - 3x^2 + 3x - 100
f^{'}(x) = 3x^2 - 6x + 3
             = 3(x^2 - 2x + 1) = 3(x-1)^2
f^{'}(x) = 3(x-1)^2
We can clearly see that for any value of x in R f^{'}(x) > 0
Hence, f (x) = x^3 - 3x^2 + 3x - 100  is an increasing function in R

Posted by

Gautam harsolia

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board 12th Exams 2026 LIVE: Class 12 political science exam begins; questions with solutions soon
anam-khan

CBSE Class 12 Economics Analysis: Students find exam moderately difficult; questions mostly application-based
anam-khan

CBSE Board Exam Analysis 2026 LIVE: Class 12 economics paper 'moderate to difficult level'; updates

Latest Question