Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma math class class 12 chapter Mean value theorem exercise 14.1 question 2 sub question (i)

Provide solution for RD Sharma math class class 12 chapter Mean value theorem exercise 14.1 question 2 sub question (i)

Answers (1)

Answer:

               c = 4 \in (2,6) , Hence, Rolle’s Theorem is verified.

Hint:

f(x) is continuous for all x and hence continuous in [2,6]

Given:

               f(x) = x^2 -8x +12 on [2,6]

Explanation:

We have

               f(x) = x^2 -8x +12

  1. Being polynomial f(x) is continuous for all x and hence continuous in [2,6]
  2. f'(x) = 2x -8 , which exists in [2,6]

              \therefore f(x)is derivable in  (2,6)

       3.

            \\f(2) = (2) ^2 - 8(2) + 12 \\\\= 4- 16 +12 = 12 + 12 = 0 \\\\ f (6) = (6) ^ 2 - 8 (6) + 12 \\\\ 36 - 48 +12 \\\\ = -12 + 12 = 0 \\\\ \therefore f(2) = f (6)

Thus all the conditions of Rolle’s Theorem are satisfied.

There exists at least onec \in (2,6)such thatf' (c) = 0

\\ \Rightarrow 2c- 8 = 0 \\\\ \Rightarrow 2c = 8 \\\\ \Rightarrow c = 4 \\\\ \therefore c = 4 \in (2,6 )

Hence, Rolle’s Theorem is verified.

Posted by

infoexpert22

View full answer

Similar Questions

Latest Question