1. ## Locating absolute extrema

Locate the absolute extrema of the function on the closed interval: f(x)= cos PIx on [1/2 , 4/3]

I will be very greatful if someone helped me understand what i must do

2. ## re: Locating absolute extrema

Originally Posted by zully32
Locate the absolute extrema of the function on the closed interval: f(x)= cos PIx on [1/2 , 4/3]

I will be very greatful if someone helped me understand what i must do
Global maxima and minima can occur at endpoints or stationary points.

Can you evaluate the function at the endpoints? Can you use calculus to evaluate the stationary points?

3. ## re: Locating absolute extrema

Originally Posted by zully32
Locate the absolute extrema of the function on the closed interval: f(x)= cos PIx on [1/2 , 4/3]

I will be very greatful if someone helped me understand what i must do
You should know that relative extrema occur at critical values. So let me ask you ... what are critical values and how does one find them?

Where else may absolute extrema exist on a closed interval?

4. ## Re: Locating absolute extrema

Ok this going to take me a while because i am use to take math in spanish but ill manage to understand you ... anyway .....the end points are the points in which the graph ends ?

5. ## Re: Locating absolute extrema

Originally Posted by zully32
Ok this going to take me a while because i am use to take math in spanish but ill manage to understand you ... anyway .....the end points are the points in which the graph ends ?
Yes. What is the value of the function at each of the endpoints?

[1/2,4/3]

7. ## Re: Locating absolute extrema

What is the value of the function at each of the endpoints?
Originally Posted by zully32
[1/2,4/3]
no, the function values at the endpoints are $f\left(\frac{1}{2}\right)$ and $f\left(\frac{4}{3}\right)$