[" given "by=(2x-1)^(2)+3],[" (i) "f(x)=-(x-1)^(2)+10]

Find the points of local maximinima of following functions (i) f(x) =(2'-1)(2'-2)^(2) " "(ii) f(x) =-(x-1)^(3) (x+1)^(2) (iii) f(x) =xenx

Find the maximum and minimum values, if any, of the following functions given by(i) f(x)=(2x-1)^2+3 (ii) f(x)=9x^2+12 x+2 (iii) f(x)=-(x-1)^2+10 (iv) g(x)=x^3+1

Let f: RvecRf(x)=x^3-3x^2+3x-2, then f^(-1)(x) is given by 1+(x+1)^(1/3) (2) 1+(x-1)^(1/3) x+1 3-1 (4) x-1 3-1

Find the derivative of f from the first principles, where f is given by(i) f(x)=(2x+3)/(x-2) (ii) f(x)=x+1/x

Find 'c' of the mean -value theorem for the functions (i) f(x) = 2x^(2) - 10x + 29 " in " [2, 7] (ii) f(x) = x ( x -1) (x -2) " in " [0, (1)/(2)]

Discuss the applicability of Rolle's theorem to the functions : (i) f(x) = x^(2) "in " [1, 2] (ii) f(x) = x^(2//3) " in " [-1, 1]

Find the domains and ranges of the real valued functions: (i) f(x) =1/(2x+1) , (ii) f(x) = (2+x)/(2-x) (iii) f(x) =x/(2-3x)

Find domain(i) f(x) = (1)/(x - 5) (ii) f(x) = (3 - x)/(x - 3) (iii) f(x) = (x^(2) - 1)/(x - 1) (iv) f(x) = (| x - 3 |)/(x - 3) (v) f(x) = (1)/(2 - sin 3x)