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

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

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

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

f(x)=(x-2)|x-3| is monotonically increasing in (a) (-oo,5/2)uu(3,oo) (b) (5/2,oo) (c) (2,oo) (d) (-oo,3)

Solve x^3-3x^2-9x-5

f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasing (b)is monotonically decreasing (c)has a point of maxima (d)has a point of minima

f(x)=[x] is step-up function. Is it a monotonically increasing function for x in R ?

f(x)=(x-8)^4(x-9)^5,0lt=xlt=10 , monotonically decreases in ((76)/(9, 10)] (b) ((8, 76)/9) (0,8) (d) ((76)/9, 10)

Prove that the function given by f(x) = x^(3) – 3x^(2) + 3x – 100 is increasing in R.