If the function `f(x)=k x^3-9x^2+9x+3` is monotonically increasing in every interval, then (a) `k<3` (b) `klt=3` (c) `k >3` (d) `kgeq3`

Options

A. `k lt 3`
B. ` j le 3`
C. `k gt 3`
D. `k ge 3`

Answer

C

Explanation

Given f(x) =`jk^(3)-9x^(2)+9x+3`
On differentiating w.r.t x we get
f(x) `=3kx^(2)-18x+9` ltbvrgt For a function to be monotonically increasing
`b^(2)-4ac lt 0`
Here a=3k,b =-18 c=9
`therefore (b^(2)-4ac=(-18)^(2)-4(3k)(9)=(-18)(-18)-3k)18xx2`
`rarr 36-12k lt0`
`rarr k gt 3`