The c of Cauchy mean value theorem for the functions f(x)=x², g(x) = x² on [12] is?
- 14/9
- 1
- 0
- -1
Explanation
The Cauchy Mean Value Theorem states that if functions f(x) and g(x) are continuous on the closed interval [a, b] and differentiable on the open interval (a, b), then there exists a point c in (a, b) such that: (f(b) - f(a))g'(c) = (g(b) - g(a))f'(c)
In this case, f(x) = x², g(x) = x², and the interval is [1, 2]. Plugging in the values, we get: (4 - 1)(2c) = (4 - 1)(2c)
Simplifying, we get: c = 14/9
So, the value of c is 14/9.
Related MCQs
- {1}
- {-1}
- {0}
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
- -72
- -60
- -48
- None of these
اس سوال کو وضاحت کے ساتھ پڑھیں
