Question:
The least and greatest values of f(x) = x3 – 6x2 + 9x in [0, 6], are
The least and greatest values of f(x) = x3 – 6x2 + 9x in [0, 6], are
Options:
- 3,6
- 0,3
- 0,6
- none of these
- 3,6
- 0,3
- 0,6
- none of these
Correct Answer: d)
Explanation:
. 3 2
1 Gi√en: f(x) =x” – 6x” + 9x
‘ f(x) =3x%- 12x +9
‘ For a local maxima or a local minima, we must ha√e
f(x)=0
‘ = 3×2 -12x+9=0
! = x2-4x+3=0
= (x-1)(x-3)=0 1
‘ =x=1,3
Now,
‘ 0) = 0% – 6(1)2 + 9(1) + 9(1) = 1- 6+ 9 = 4 ‘
‘ f(c)=13-6(12+9(1)=1-6+9=4
3)=3%-6(3)° +93) = 27-54 +27=0
‘ (6) = 6° – 6(6)% + 9(6) = 216 – 216 + 54 = 54 ‘
‘ The least and greatest √alues of f(x) = x – 6×2 + 9x in 0, 6 are 0 and 54, respecti√ely. ‘
. 3 2
1 Gi√en: f(x) =x” – 6x” + 9x
‘ f(x) =3x%- 12x +9
‘ For a local maxima or a local minima, we must ha√e
f(x)=0
‘ = 3×2 -12x+9=0
! = x2-4x+3=0
= (x-1)(x-3)=0 1
‘ =x=1,3
Now,
‘ 0) = 0% – 6(1)2 + 9(1) + 9(1) = 1- 6+ 9 = 4 ‘
‘ f(c)=13-6(12+9(1)=1-6+9=4
3)=3%-6(3)° +93) = 27-54 +27=0
‘ (6) = 6° – 6(6)% + 9(6) = 216 – 216 + 54 = 54 ‘
‘ The least and greatest √alues of f(x) = x – 6×2 + 9x in 0, 6 are 0 and 54, respecti√ely. ‘