Question

What are the relative minimum and relative maximum values over the interval [−4,4] for the function shown in the graph?

relative minimum = −36 , relative maximum = 64

relative minimum = −3 , relative maximum = −36

relative minimum = 0, relative maximum = 64

relative minimum = −3 , relative maximum = 64



The table of values represents a polynomial function ​f(x)​.

How much greater is the average rate of change over the interval [5,7] than the interval [2, 4] ?

2 39
3 125
4 287
5 549
6 935
7 1469
Enter your answer in the box.

Answer 1

The relative minimum would be the Y value of the lowest point of the curved the line which is -36.

The relative maximum would be the Y value of the highest point of the curved line which is at 64.

Answer: relative minimum = −36 , relative maximum = 64

Rate of change between [5,7]

At 5 y = 549 at 7 y = 1469

Rate of change = change in y over change in x:

1469 - 549 / 7-5 = 920/2 = 460

Rate of change between [2,4]

At 2 y = 39, at 4 y = 287

Rate of change:

287 - 39 / 4-2 = 248/2 = 124

Now subtract the two: 460 - 124 = 336 greater

Answer 2

Relative minimum : -36

Relative maximum : 64

The rate of change is 336 greater

Explanation:

Relative minimum are the minimum values in the interval

Looking at the graph, we find the lowest point in the interval

Relative minimum : (-3, -36) and (3,-36) y value -36

Looking at the graph, we find the highest point in the interval

Relative maximum : (0,64) y value 64

Average rate of change = f(x2) - f(x1)

---------------

x2 - x1

f(7) - f(5) 1469 - 549 920

------------- = --------------- = ------- = 460

7-5 7-5 2

f(4) - f(2) 287 - 39 248

------------- = --------------- = ------- = 124

4-2 4-2 2

We need to subtract

460-124

336