# Max and Min Values

• Jan 5th 2008, 05:24 PM
johntuan
Max and Min Values
Without graphing, find the absolute max and min values.

f(x)=3x+2 for XE[-1,1]

I know this is easy but when i take the derrivative i get f'(x)=3. and then i am stuck from there, what would i do next?
• Jan 5th 2008, 05:31 PM
Jhevon
Quote:

Originally Posted by johntuan
Without graphing, find the absolute max and min values.

f(x)=3x+2 for XE[-1,1]

I know this is easy but when i take the derrivative i get f'(x)=3. and then i am stuck from there, what would i do next?

remember, for absolute max and min, you also test the end points. since the derivative is never zero, it is not even a candidate for the absolute max or min. so just find the values of the function at the end points, the larger one is the absolute max, the smaller is the absolute min
• Jan 5th 2008, 05:36 PM
Soroban
Hello, johntuan!

Quote:

Without graphing, find the absolute max and min values.
. . $\displaystyle f(x) \:=\:3x+2\;\text{ for }x \in [-1,1]$

I take the derrivative and get: .$\displaystyle f'(x)\,=\,3$
What would i do next?

Since the derivative is never zero, there is no relative max or min anywhere.

Then we must test the endpoints of the interval.

. . $\displaystyle \begin{array}{cccccc}f(\text{-}1) &=& 3(\text{-}1)+2 &=& \text{-}1 & \text{abs. minimum} \\ f(1) &=& 3(1)+2 &=& 5 & \text{abs. maximum}\end{array}$