NIELIT 2016 MAR Scientist B - Section B: 5

Question

The greatest and the least value of 

$f(x)=x^4-8x^3+22x^2-24x+1$ in $[0,2]$ are

• A. $0,8$
• B. $0,-8$
• C. $1,8$
• D. $1,-8$

Answer 1

We can use synthetic division if one of the root is known. Vieta's formula for cubic polynomial can also be used, but I found this one easier. 

Confirming with Desmos

Answer 2

Answer should be D,

The max value of the given expression will be when x=0 and the minimum value will be when x=2