Which of the following is not a necessary condition for Cauchy's Mean Value Theorem?
- The derivation of g(x) be equal to 0
- The functions, f(x) and g(x) be continous in [a,b]
- The functions f(x) and g(x) be derivable in (a, b)
- None of these
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).
Related MCQs
- Odd function
- Even function
- Constant symmetric form
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- Factoring the polynomial
- Finding the derivative
- Substituting the value of x
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- x = 2, −1/2
- x = 1, −2
- x = 3, −1
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- Commutative
- Associative
- Distributive
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
