" 1."(i)quad f(x)=x(x-2)" in "[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 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 domain of the following: (i) f(x) = (1)/(log_(10) (1-x)) + sqrt(x+2) (ii) f(x) = sqrt(1-2x) + 3 sin^(-1) ((3x-1)/(2))

Which of the following is/are true? I. The derivative of f(x)=1+x+x^(2)+.....+x^(50) at x=1 is 1250. II. The derivative of f(x)=(x+1)/(x)" is "1/x^(2) .

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)

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)

Draw the graphs of the linear funcations (i) f (x) = 1 -x (ii) f(x) = 2x+1

Let f:[0,1]toR (the set of all real numbers ) be a function. Suppose the function f is twice differentiable,f(0)=f(1)=0 and satisfies f''(x)-2f'(x)+f(x)gee^(2),x in [0,1] Consider the statements. I. There exists some x in R such that, f(x)+2x=2(1+x^(2)) (II) There exists some x in R such that, 2f(x)+1=2x(1+x)

Let f : R to R be continuous function such that f (x) + f (x+1) = 2, for all x in R. If I _(1) int_(0) ^(8) f (x) dx and I _(2) = int _(-1) ^(3) f (x) dx, then the value of I _(2) +2 I _(2) is equal to "________"

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .