Question

Find the critical points of the function f(x) `=4x^(3)-6x^(2) -24x+9 " if f(i) x in [0,3] (ii) x in [-3,3] (iii) x in [-1,2]`

Answer 1

` f(x) =12(x^(2) -x-2)`
`=12 (x-2) (x+1)`
`f(x) =0 " "rArr " "x=- 1 " or " 2`
`(i) if x in [0,3] x=2 " is critical point "`
`(ii) " if " x in [-3,3] " then we have two critical points " x =- 1,2`
`(iii) " if "Xin [- 1,2] " then no critical point as both " x=-1 " and " x=2 " become boundary points "`
Note : Critical points are always interior points of an interval.