Let `f'(x) = (x^2-x+ 2)(x^2-x-2)(x^2-x-6) (x^2-x-12), x in R,` then

Let f(x)= x^4- 3x^3 + 2x^2-3x+ a .If f(sqrt-1)= 0 and a in R then prove that f (x) < 0 for x in (1,2) .

Let f(x) = (x^2 - x)/(x^2 + 2x) , then d/(dx) (f^(-1)(x))^(-) is equal to

Let f(x) ={{:((x^(3)+x^(2)-16x+20)//(x-2)^(2)"," if x ne 2),(R", "if x = 2):} If f(x) is continuous for all x, then k = … .

Let f(x)=2x-tan^-1 x- ln(x+sqrt(1+x^2)); x in R, then

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...... .

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...... .

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...... .

Let f(x)=(x^(2)-x)/(x^(2)+2x) then d(f^(-1)x)/(dx) is equal to

Let f(x)=(x^2-x)/(x^2+2x) then d(f^(-1)x)/(dx) is equal to