If `\ ^(24)C_x=\ ^(24)C_(2x+3) ` find x

Find the product 24x^(24)(1 - 2x) and evaluate it for x = 2.

Find the product 24x^(2)(1-2x) and evaluate its value for x=3.

Find the absolute maximum and minimum values of f(x) = 2x^(3) - 24x + 57 in the interval [1, 3].

Find the absolute maximum value of f(x) = 2x^(3) - 24x + 107 in the interval [1, 3].

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].