8. f (c) = (x - 2) 4 (x - 3) 3, in the interval [2, 3] - 19.fr) in Shanal

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].

Verify Rolle's theorem for the following functions in the given intervals. f(x) = (x-2)^(4) (x-3)^(3) in the interval [2,3].

Verify Rolle's theorem for the following functions in the given intervals. f(x) = (x-2)^(4) (x-3)^(3) in the interval [2,3].

The greatest value of the function f(x)=2. 3^(3x)-3^(2x). 4+2. 3^x in the interval [-1,1] is

The greatest value of the function f(x)=2.3^(3x)-3^(2x).4+2.3^(x) in the interval [-1,1] is

Find the intervals in which f(x) = 2x^(3) - 9x^(2) - 12 x -3 is increasing and the intervals in which f(x) is decreasing.

f(x)=(x-2)(x-3)(x-4) interval [2,4]

If f:R rarr R and g : R rarr R are defined by f(x) = 3x + 2 and g(x) = x^2 - 3 , then the value of x such that g(f(x))=4 are