1. ## Absolutes

Find the absolute maximum and minimum values of the following function on the interval [1,3]

$
f(x) = \frac{4x^2+9}{x}
$

Do i make a table of values or what do i do?
Thanks to everyone who helps

2. what do you know about derivatives? ... i.e., what they can tell you about the behavior of a function.

3. Originally Posted by qzno
Find the absolute maximum and minimum values of the following function on the interval [1,3]

$
f(x) = \frac{4x^2+9}{x}
$

Do i make a table of values or what do i do?
Thanks to everyone who helps
The absolute maximum and minimum will either be where the derivative is 0, or on the endpoints.

The endpoints are

$f(1) = 13$ and $f(3) = 15$

The derivative is

$f'(x) = \frac{4x^2 - 9}{x^2}$ (use the Quotient rule).

Set this equal to 0 and solve for x.

$0 = \frac{4x^2 - 9}{x^2}$

$0= 4x^2 - 9$

$0 = (2x + 3)(2x - 3)$

$2x+3 = 0$ or $2x - 3= 0$

$x = -\frac{3}{2}$ or $x = \frac{3}{2}$.

Substitute these values back into f(x) to determine their corresponding y-values.

$f(\frac{3}{2}) = 12$, $f(-\frac{3}{2}) = -12$.

So the absolute maximum is 15 which occurs at x = 3, and the absolute minumum is -12 and occurs at x = $-\frac{3}{2}$.

4. how is $x = -\frac{3}{2}$ on the interval [1,3] ?

5. Originally Posted by qzno
how is $x = -\frac{3}{2}$ on the interval [1,3] ?
Oops - my mistake :P.

That means the minimum is actually 12 and occurs at $x = \frac{3}{2}$

6. ohh ok thanks !