EMC Q.40
0. The greatest and least value of f(x) = x4- 8x3 + 22x2 - 24x +1 in [0, 2] are
- Option : D
- Explanation : f(x) = x4- 8x3 + 22x2 - 24x +1 , f(0) = 1
f(2) = 24 - 8.23 + 22.22 - 24.2 + 1 = -7
Now f ' (x) = 4x3-24x2 + 44x - 24
For maximum and minimum, f ' (x) = 0
⇒ 4x3-24x2 + 44x - 24 = 0
⇒ 4(x - 1)(x - 2)(x - 3) = 0
therefore x = 1, 2, 3
Since x = 3 doesnot lie in [0, 2]
therefore, consider only x = 1 and x = 2
We have f(1) = 14 - 8.13 +22.12 - 24.1 + 1 = -8
Greatest of f(x) = largest of {1, -7, -8} = 1
Least of f(x) = smallest of {1, -7, -8} = -8
