Find the absolute maximum of the function `f(x)=x^3+3x^2-9x+7` in the interval `[-4,2]`.

Find the maximum value of the function f(x)=5+9x-18x^(2)

Find c of Lagranges mean value theorem for the function f(x)=3x^(2)+5x+7 in the interval [1,3].

Verify Rolle's theorem for the function f(x)=x^(3)-3x^(2)+2x in the interval [0,2] .

The function f(x)=2x^3+9x^2+12x+20 is increasing in the interval

Verify Rolle's theorem for the function f(x) = x^(3) - 9x^(2) + 26x -24 in the interval [2.4]

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

If rolle's theorem is applicable to the function f(x)=x^(3)-2x^(2)-3x+7 on the interval [0,k] then k is equal

Find the absolute maximum and the absolute minimum values of the following function in the given intervals: f(x)=(x-2)sqrt(x-1) in [1,9]

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 maximum and minimum values of f(x)=2x^(3)-24x+107 in the interval [1,3]