" (b) "f(x)=x+(1)/(x),quad " interval "[(1)/(2),3]

f(x)=log x, interval [1,e]

f(x)=|x|, interval [-1,1]

Find the value of c, of mean value theorem.when (a) f(x) = sqrt(x^(2)-4) , in the interval [2,4] (b) f(x) = 2x^(2) + 3x+ 4 in the interval [1,2] ( c) f(x) = x(x-1) in the interval [1,2].

Using Lagrange's theorem , find the value of c for the following functions : (i) x^(3) - 3x^(2) + 2x in the interval [0,1/2]. (ii) f(x) = 2x^(2) - 10x + 1 in the interval [2,7]. (iii) f(x) = (x-4) (x-6) in the interval [4,10]. (iv) f(x) = sqrt(x-1) in the interval [1,3]. (v) f(x) = 2x^(2) + 3x + 4 in the interval [1,2].

For the function f(x) = x cosx 1/x, x ge 1(A) for at least one x in the interval [1, c), f(x +2)-fx) 2 (B) lim f(x)= 1 (C) for all x in the interval [1, co), f(x +2)-f(x)> 2 (D) f (x) is strictly decreasing in the interval [1, co) lim fix )=

If f(x) = (1)/(2) x - 1 , then on the interval [0, pi] :

Let f(x)=x^(3)+(1)/(x^(3)), Ift the intervals in which f(x) increases are (oo,a] and [b,oo) then min(b-a) is =

If f(x)=(9x)/(x+2)f or x 1, then in the interval (-3,3) function is