Get Advice on Live Video Call
Earn $ Cash $ with
consultations on Bissoy App

Mean Value theorem is applicable to the and continuous in open interval (a, b) b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) d) Functions differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’

Correct Answer: a, b
Statement of Mean Value Theorem is that, If function f(x) is continuous in closed interval and differentiable in open interval (a, b), then there exists a point ‘c’ such that c∈(a,b) and f’(c) = /(b-a).

Rolle’s theorem is applicable to the and continuous in open interval (a, b) only and having same value at point ‘a’ and ‘b’ b) Functions continuous in closed interval only and having same value at point ‘a’ and ‘b’ c) Functions continuous in closed interval and differentiable in open interval (a, b) only and having same value at point ‘a’ and ‘b’ d) Monotonically Increasing funtions

The mixing vat in a factory receives liquid ingredients through six separate value--- labeled R.S.T.U,Y and Z -- each of which has exactly two settings: open and closed.The mixing vat operator must ensure that each valve is set open or closed according to the following conditions: If T is open, both S and Z must be closed, R and Z cannot both be closed at the same time; If Y is closed, Z must also be closed;S and U cannot both be open at the same time. If the maximum number of valves that can be closed at the same time are closed which of the following must true?

The mixing vat in a factory receives liquid ingredients through six separate value--- labeled R.S.T.U,Y and Z -- each of which has exactly two settings: open and closed.The mixing vat operator must ensure that each valve is set open or closed according to the following conditions: If T is open, both S and Z must be closed, R and Z cannot both be closed at the same time; If Y is closed, Z must also be closed;S and U cannot both be open at the same time. If R is closed and U is open, which of the following must be true?

The mixing vat in a factory receives liquid ingredients through six separate value--- labeled R.S.T.U,Y and Z -- each of which has exactly two settings: open and closed.The mixing vat operator must ensure that each valve is set open or closed according to the following conditions: If T is open, both S and Z must be closed, R and Z cannot both be closed at the same time; If Y is closed, Z must also be closed;S and U cannot both be open at the same time. If Z is open, which of the following must be true?

The mixing vat in a factory receives liquid ingredients through six separate value--- labeled R.S.T.U,Y and Z -- each of which has exactly two settings: open and closed.The mixing vat operator must ensure that each valve is set open or closed according to the following conditions: If T is open, both S and Z must be closed, R and Z cannot both be closed at the same time; If Y is closed, Z must also be closed;S and U cannot both be open at the same time. Which of the following, if given to the mixing vat operator as an instruction, would not determine the setting of any other valve ?

Seven people A, B, C, D, E, F and G live on separate floors of a 7-floor building. Ground floor is numbered 1, first floor is numbered. 2 and so on until the topmost floor is numbered 7. Each one of these having a different cars-Cadillac, Ambassador, Fiat, Maruti, Mercedes, Bedford and Fargo but not necessarily in the same order. Only three people live above the floor on which A lives. Only one person lives between A and the one having a car Cadillac. F lives immediately below the one having a car Bedford. The one having a car Bedford lives on an even-numbered floor. Only three people live between the ones having a car Cadillac and Maruti. E lives immediately above C. E is not having a car Maruti. Only two people live between B and the one having a car Fargo. The one having a car Fargo lives below the floor on which B lives. The one having a car Fiat does not live immediately above D or immediately below B. D does not live immediately above or immediately below A. G does not have a car Ambassador. Question : How many people live between the floors on which D and the one having a car Bedford ?

Given the following statements about a function f : R → R , select the right option:
P: If f(x) is continuous at x = x0, then it is differential at x = x0.
Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0.
R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0.

Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. How far and in which direction is Point G from Point A?

Study the following information and answer the questions. Point A is 8m to the west of Point B. Point C is 4m to the south of Point B. Point D is 4m to the east of Point C. Point F is 6m to the north of Point D. Point E is 8m to the west of Point F. Point G is 2m to the south of Point E. If point G is 4m to the north of Point H, then what is the distance between H and D?

Find the value of ‘a’ if f(x) = ax2+32x+4 is continuous over and differentiable over (-4, 0) and satisfy the Rolle’s theorem. Hence find the point in interval (-2,0) at which its slope of a tangent is zero