Absolute Extrema of 2x - (x-2) on [0,1], [-3,4]

In summary, the conversation discusses finding the absolute extrema of the function f(x) = {2x} - {x-2} on the given intervals [0,1] and [-3,4]. It is suggested to take the derivative and break the function into smaller intervals to find the extrema. The concept of a piecewise function is also mentioned as a possible approach.
  • #1
portillj
9
0
{} these brackets are going to represent the absolute value lines
the problem states
find the absolute extrema of the given function on each individual interval:
f(x)= {2x} - {x-2}
a) [0,1]
b) [-3, 4]

I know I need the derivative of the equation but it does not really give a good derivative since it would be f'(x)= 2 - {1}
 
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  • #2
well, first what is {2x} equal to when x is from [0,1], als owhat is the value of {x-2}, do the same thing in the other interval!
 
  • #3
You could also break the function up into the intervals [itex](-\infty,0)[/itex], [itex][0,2)[/itex], and [itex][2,\infty)[/itex] and write f as a piecewise function. Then, you can find the derivative on each of those open intervals (remember that the derivative won't necessarily be defined at 0 and 2).
 
  • #4
how am i suppose to do tat
 
  • #5
portillj said:
how am i suppose to do tat

Do u know how a piecewise defined function looks like? Well, to do that in this case you need to follow both my hints and also PingPong's hints!
 

FAQ: Absolute Extrema of 2x - (x-2) on [0,1], [-3,4]

1. What is the definition of absolute extrema?

The absolute extrema of a function is the highest and lowest values that the function takes on a specific interval. These values can be found by analyzing the endpoints of the interval and any critical points within the interval.

2. How do you find absolute extrema on a closed interval?

To find absolute extrema on a closed interval, you need to evaluate the function at the endpoints of the interval and any critical points within the interval. The highest and lowest values from these evaluations will be the absolute extrema.

3. What are critical points?

Critical points are values of a function where the derivative is either equal to zero or undefined. These points can indicate the location of maximum or minimum values of a function.

4. How do you determine if a critical point is a maximum or minimum?

To determine if a critical point is a maximum or minimum, you can use the first or second derivative test. The first derivative test looks at the sign of the derivative on either side of the critical point, while the second derivative test looks at the concavity of the function at the critical point.

5. How do you apply these concepts to the given function 2x - (x-2) on [0,1], [-3,4]?

To find the absolute extrema of the given function on the intervals [0,1] and [-3,4], you will need to evaluate the function at the endpoints (0, 1, -3, 4) and any critical points within the intervals. Once you have these values, you can determine the highest and lowest values, which will be the absolute extrema of the function on the given intervals.

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