
9-1
9
Mean Value Theorems
L e a rnin g Obje c ti v e s
After reading this chapter, you will be conversant with:
♦ Rolle’s Theorem
♦ Mean Value Theorem or Lagrange’s Mean Value Theorem
♦ Cauchy’s Mean Value Theorem
♦ Generalised Mean Value Theorem
Introduction
The mean value theorem is one of the most essential tools in calculus and used to prove a host of other
theorems in Differential and Integral Calculus. In this chapter, we shall discuss in detail some of the
important theorems in calculus namely Rolle’s theorem, Lagrange’s theorem, Cauchy’s mean value
theorem and Generalised mean value theorems.
9.1 ROLLE’S THEOREM
Rolle’s theorem is an important ...