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f(x) = In (x – 3), [4,6]

f(x) = In (x – 3), [4,6]

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
The task is to find the value or values of \( c \) that satisfy the given function and interval. **Function:** \[ f(x) = \ln(x - 3) \] **Interval:** \[ [4, 6] \] **Note:** - You are required to type an exact answer and use a comma to separate multiple answers. - Enter the value of \( c \) in the provided box: \[ c = \boxed{\phantom{answer}} \]
Transcribed Image Text:The task is to find the value or values of \( c \) that satisfy the given function and interval. **Function:** \[ f(x) = \ln(x - 3) \] **Interval:** \[ [4, 6] \] **Note:** - You are required to type an exact answer and use a comma to separate multiple answers. - Enter the value of \( c \) in the provided box: \[ c = \boxed{\phantom{answer}} \]
Expert Solution
Step 1

Given:

    fx=lnx-3 , 4,6

  The function lnx-3 is defined and continuous for all x>3

     By mean value theorem :

               f'(c)=f(b)-f(a)b-a

       f(x)=ln(x-3)

      f'(x)=ddxln(x-3)

         f'(x)=1x-3

        f'(c)=1c-3

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