Enroll in one of our FREE online STEM bootcamps. Join today and start acing your classes!View Bootcamps

University of California, Riverside

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52
Problem 53
Problem 54
Problem 55
Problem 56
Problem 57
Problem 58
Problem 59
Problem 60
Problem 61
Problem 62
Problem 63
Problem 64
Problem 65
Problem 66
Problem 67
Problem 68
Problem 69
Problem 70
Problem 71
Problem 72

Problem 41

a. Identify the function's local extreme values in the given domain, and say where they occur.

b. Which of the extreme values, if any, are absolute?

c. Support your findings with a graphing calculator or computer grapher.

$$

f(x)=2 x-x^{2}, \quad-\infty<x \leq 2

$$

Answer

See the graph

You must be logged in to like a video.

You must be logged in to bookmark a video.

## Discussion

## Video Transcript

get some four problem 41. We work even the function FX, which is equal to two X minus X squared. So to answer the first part A In this problem, we need to take derivative of dysfunction, which is to minus two X and we let this derivative to be positive. Then we can find that X is smaller than one. So that means from next infinity to one, dysfunction will be increasing. And from 1 to 2, this function will be decreasing. And hence F one will be our loco extreme. Okay, Now, for part B need to identify whether the local stream here is is absolute the way to check. It's just Ah, um, check the maximum value off this whole entire function. Um, well, in this case, we there are two values that we need to check adversities to act one where that one is two minus one, which is one and the other. The other body we need a chap is the endpoint, which is to we'll have to be people plugging X equals two into our function. We will have zero. But dysfunction, as we know, is a parabola. So from so wouldn't x is equal to one. We reach our Mexico. And when we well, we checked the interval from 1 to 2, then it will be look like where it would be like this. So that means that one, it's the absolute maximum, which may say the except it is at his absolute.