In the interval [2, 5], the function $x^2-6 x+9$
A. is strictly increasing
B. is strictly decreasing
C. has absolute minima at x = 2
D. has absolute maxima at x = 5
E. never attains a negative value.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → D, E only
$f(x)=x^2-6x+9=(x-3)^2$
$f'(x)=2(x-3)$
$f'(x)<0 \text{ for } x<3,\;\; f'(x)>0 \text{ for } x>3$
$\text{Hence not strictly increasing or decreasing on } [2,5]$
$f(2)=1,\;\; f(3)=0,\;\; f(5)=4$
$\text{Minimum at } x=3,\;\; \text{maximum at } x=5$
$f(x)\ge 0 \text{ for all } x$
The correct statements are D and E.