Lagrange Theorem Questions Solution3

In this page Lagrange theorem questions solution3 we are going to see solution of the practice questions.

(iv) f (x) = x ^(2/3) , [-2 , 2]

Solution:

If f (x) be a real valued function that satisfies the following conditions.

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(v) f (x) = x³ - 5 x² - 3 x , [1 , 3]

Solution:

If f (x) be a real valued function that satisfies the following conditions.

f (x) = x³ - 5 x² - 3 x

f ' (x) = 3 x² - 5 (2 x) - 3

f ' (x) = 3 x² - 10 x - 3

f ' (c) = 3 c² - 10 c - 3

f (1) = x³ - 5 x² - 3 x

        = (1)³ - 5 (1)² - 3 (1)

        = 1 - 5 - 3

        = - 7

f (1) = - 7

f (3) = x³ - 5 x² - 3 x

       = (3)³ - 5 (3)² - 3 (3)

       = 27 - 45 - 9

       = 27 - 54

       = -27

f (3) = - 27

f ' (c) = f (b) - f (a) / (b - a)

         = [-27 - (-7)]/(3 - 1)

         = [-27 + 7]/2

         = -20/2

         = -10

3 c² - 10 c - 3  = -10 

3 c² - 10 c - 3 + 10 = 0

 3 c² - 10 c + 7 = 0

 3 c² - 3 c - 7 c - 7 = 0

 3 c (c - 1) - 7 (c - 1) = 0

(c - 1) (3 c - 7) = 0

 c - 1 = 0              3 c - 7 = 0

    c = 1                  3 c = 7

                                c = 7/3   Lagrange theorem questions solution3

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• First Principles 
• Implicit Function
  
• Parametric Function
• Substitution Method
  
• logarithmic function
  
• Product Rule
  
• Chain Rule
  
• Quotient Rule
• Rate of Change
• Rolle's theorem
• Lagrange's theorem
• Finding increasing or decreasing interval
  
• Increasing function
  
• Decreasing function
• Monotonic function
• Maximum and minimum
• Examples of maximum and minimum