If `f(x)=k x^3-9x^2+9x+3` monotonically increasing in `R ,` then (a)`k<3` (b) `klt=2` (c)`kgeq3` (d) none of these

Function f(x)=2x^3-9x^2+12 x+29 is monotonically decreasing when (a) x 2 (c) x >3 (d) x in (1,2)

Function f(x)=x^3-27 x+5 is monotonically increasing when (a) x 3 (c) xlt=-3 (d) |x|geq3

Let f(x) be and even function in R. If f(x) is monotonically increasing in [2, 6], then

Find the values of k for which f(x)=k x^3-9k x^2+9x+3 is increasing on R .

If the function f(x)=x^3-9k\ x^2+27 x+30 is increasing on R , then (a) -1lt=k 1 (c) 0

If f(x)={{:(-e^(-x)+k,",",xle0),(e^(x)+1,",",0ltxlt1),(ex^(2)+lambda,",",xge1):} is one-one and monotonically increasing AA x in R , then

if f(x) =2e^(x) -ae^(-x) +(2a +1) x-3 monotonically increases for AA x in R then the minimum value of 'a' is

If f(x) is monotonically increasing function for all x in R, such that f''(x)gt0andf^(-1)(x) exists, then prove that (f^(-1)(x_(1))+f^(-1)(x_(2))+f^(-1)(x_(3)))/(3)lt((f^(-1)(x_(1)+x_(2)+x_3))/(3))

Let f(x)=|x^2-3x-4|,-1lt=xlt=4 Then f(x) is monotonically increasing in [-1,3/2] f(x) monotonically decreasing in (3/2,4) the maximum value of f(x)i s(25)/4 the minimum value of f(x) is 0

Let set of all possible values of lamda such that f (x)= e ^(2x) - (lamda+1) e ^(x) +2x is monotonically increasing for AA x in R is (-oo, k]. Find the value of k.