Question

Mean Value Theorem tells about the

(a) Existence of point c in a curve where slope of a tangent to curve is equal to the slope of line joining two points in which curve is continuous and differentiable

(b) Existence of point c in a curve where slope of a tangent to curve is equal to zero

(c) Existence of point c in a curve where curve meets y axis

(d) Existence of point c in a curve where curve meets x axis

The question was asked in a job interview.

This interesting question is from Lagrange’s Mean Value Theorem topic in chapter Differential Calculus of Engineering Mathematics

Answer 1

The correct answer is (a) Existence of point c in a curve where slope of a tangent to curve is equal to the slope of line joining two points in which curve is continuous and differentiable

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