Which of the following is not a necessary condition for Cauchy's Mean Value Theorem?
Answer: The derivation of g(x) be equal to 0
Explanation
Cauchy's Mean Value Theorem states that if two functions f(x) and g(x) are continuous on the closed interval [a, b] and differentiable on the open interval (a, b), and g'(x) ≠ 0 for any x in (a, b), then there exists a point c in (a, b) such that:(f'(c) / g'(c)) = (f(b) - f(a)) / (g(b) - g(a))
The necessary conditions for Cauchy's Mean Value Theorem are:
- 1. The functions f(x) and g(x) are continuous on [a, b].
- 2. The functions f(x) and g(x) are differentiable on (a, b).
- 3. g'(x) ≠ 0 for any x in (a, b).
This question appeared in
Past Papers (4 times)
Lecturer Mathematics Past Papers and Syllabus (1 times)
SPSC 25 Years Past Papers Subject Wise (Solved) (2 times)
SPSC Past Papers (1 times)
This question appeared in
Subjects (1 times)
MATHS MCQS (1 times)
Related MCQs
- Lagrange's mean value theorem is a particular case of _____? Cauchy's mean value theorem,
- The c of Cauchy mean value theorem for the functions f(x)=x², g(x) = x² on [12] is?
- In a process, quantity or condition that the control alters to initiate change in the value of the regulated condition is
- When a gift is made subject to condition which derogrates from the completeness of grant, the condition is
- If a : b = c : d then a : c = b : d. This is the theorem of ____?
- Who invented Binomial Theorem?
- Which of the following is not the equation of Bernoulli's theorem
- According to Pythagoras theorem c = _____?
- The Mean Value Theorem was stated and proved by?
- Leibniz theorem is applicable if n is a?
