Explain why Rolle's theorem is not applicable to the following functions in the respective intervals.
`f(x)=|1/x|,x in[-1,1]`

Explain why Rolle's theorem is not applicable to the following functions in the respective intervals. f(x)=tanx,x in[0,pi]

Explain why Rolle's theorem is not applicable to the following functions in the respective intervals. f(x)=x-2logx,x in[2,7]

Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals : f(x)=(x+1)/x,x in[-1,2]

Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals : f(x)=|3x+1|,x in[-1,3]

Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals: f(x) = (x +1)/(x), x in [-1,2]

Discuss the applicability of Rolles theorem for the following functions on the indicated intervals: f(x)=|x|in[-1,1] f(x)=3+(x-2)^(2//3) in [1,3] f(x)=tanx in [0,pi] f(x)=log{(x^2+a b)/(x(a+b))} in [a,b], where 0 less than a less than b

Find the absolute extrema of the following functions on the given closed interval. f(x)=6x^(4/3)-3x^(1/3),[-1,1]

Find the absolute extrema of the following functions on the given closed interval. f(x)=x^(3)-12x+10,[1,2]