# minimum values

• Jun 11th 2008, 02:41 AM
Math Phobe
minimum values
This is a practice exam problem am stuck on(Headbang)

Find the max and min values of the fuction f(x)=x^3-9x^2+15x+3 on intervals [0,2]
• Jun 11th 2008, 02:58 AM
CaptainBlack
Quote:

Originally Posted by Math Phobe
This is a practice exam problem am stuck on(Headbang)

Find the max and min values of the fuction f(x)=x^3-9x^2+15x+3 on intervals [0,2]

The global extrema of a function on a closed interval are either calculus type local extrema in the interior of the interval or occur at the end points of the interval.

So first look at the solutions of:

$f'(x)=3x^2-18x+15=0$

these are the roots of $x^2-6x+5=0$, which are $x=5$ and $x=1$, $x=5$ is not in the interval so we can ignore it, so now we need only consider

$f(0),\ f(1)$ and $f(2),$

$f(0)=3,$
$f(1)=1-9+15+3=10$
$f(2)=8-36+30+3=5$

so the global minimum on $[0,2]$ is $3$ and the global maximum is $10$ and these occur when $x=0$ and $x=1$ respectivly.

RonL