Mean value theorem,theory and PPT Q.no.01-20

Cauchys mean value theorem

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = e^(x) in the interval [0,1].

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = tan^(-1)x in the interval [0,1]

Verify Lagrange's Mean Value theorem for the following functions in the given intervals f(x) = 1 + 2x -x^(2) in the interval [0,1] .

In [0,1] Largrange's mean value theorem is not application to

Verify mean value theorem for the function f(x) = x^(3)-2x^(2)-x+3 in [0,1]

Discuss the applicability of Lagrange's Mean Value Theorem to the following : f(x)=2x-x^(2)" in "[0,1]

Langrange mean value theorem with Illustration

Discussion PPT Q.no. 65-82

Statement I for f(x)={{:((1)/(2)-x",",xlt(1)/(2)),(((1)/(2)-x)^(2)",",xge(1)/(2)):} mean value theorem is applicable in the interval [0, 1] Statement II For application of mean value theorem, f(x) must be continuous in [0,1] and differentiable in (0, 1).