Use the mean value theorem to prove `e^xgeq1+xAAx in R`

Show that the value in the conclusion of the mean value theorem for f(x) = (1)/(x) on a closed interval of positive number [a,b] in sqrtab

Show that the value in the conclusion of the mean value theorem for f(x)=1/x on a closed interval of positive numbers [a, b] is sqrt(ab) .

Using intermediate value theorem, prove that there exists a number x such that x^(2005)+1/(1+sin^2x)=2005.

Show that the value in the conclusion of the mean value theorem for f(x)=Ax^(2)+Bx+C on any interval [a, b] is (a+b)/2

The number given by the Mean value theorem for the function 1/x,x in[1,9] is

Let f'(x)=e^(x)""^(2)and f(0)=10.If Altf(1)ltB can be concluded from the mean value theorem, then the largest volume of (A-B) equals

Using mean value theorem prove that for , a gt 0, bgt 0, |e^(-a)-e^(-b)| lt| a-b|

Verify Lagrange's mean value theorem for f(x) = (1)/(x) " in " [1, 2]

Find the values in the interval (1,2) of the mean value theorem satisfied by the function f(x)=x-x^(2) "for" 1 le x le 2 .