If `f'(x)>0 and f''(x)>0AAx inR,` then for any two real numbers `x_1 and x_2,(x_1!=x_2)`

If f'(x)>0 and f''(x)>0AA x in R, then for any two real numbers x_(1) and x_(2),(x_(1)!=x_(2))

If f'(x)>0,AA x in R, then for any two real in shers x_(1) and x_(2)(x_(1)!=x_(2))

If f''(x)>0 and Q(x)=2f((x^2)/2)+f(6-x^2),AAx in R , then function Q(x) is

If f(x)=(x)/(1+|x|)" for "x inR , then f'(0) =

If f(x)+f(1-x)=2 and g(x)=f(x)-1AAx in R , then g(x) is symmetric about

Statement-1: If alpha and beta are real roots of the quadratic equations ax^(2) + bx + c = 0 and -ax^(2) + bx + c = 0 , then (a)/(2) x^(2) + bx + c = 0 has a real root between alpha and beta Statement-2: If f(x) is a real polynomial and x_(1), x_(2) in R such that f(x_(1)) f_(x_(2)) lt 0 , then f(x) = 0 has at leat one real root between x_(1) and x_(2) .

If f is a real function such that f(x)>0,f'(xx) is continuous for all real x and axf'(x)>=2sqrt(f(x))-2af(x),(ax!=2) show that sqrt(f(x))>=(sqrt(f(1)))/(x),x>=1