In the interval `(0, 1), f(x) = x^(2) – x + 1` is -

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].

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].

In the interval (-1, 1), the function f(x) = x^(2) - x + 4 is :

In the interval (-1, 1), the function f(x) = x^(2) - x + 4 is :

For the fucntion f(x)=x cos ""1/x, x ge 1 which one of the following is incorrect ? (a)for atleast one x in the interval [1, oo), f(x + 2) - f(x) lt 2 (b) underset(x rarr oo)(lim) f'(x) = 1 (c)for all x in the interval [1, oo), f(x+2) - f(x) gt 2 (d)f'(x) is strictly decreasing in the interval [1, oo)

Find the average value of mu of the function f(x) over the indicated intervals: (a) f(x) = 2x^(2) + 1 over [0, 1] (b) f(x) = (1)/(x) over [1, 2] (c ) f(x) = 3^(x)-2x + 3 over [0, 2]

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] .

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] .