Question

Find the coordinates for the local maximum and local minimum for the graph
y=-x^5+3x^4+4x^2+1

I found the maximum but I'm unsure of my answer for the minimum.

max= (2.631, 46.370)
min=-1.2 e-6, 1

Is that right?

Answer 1

There are two tests for minimum and maximum:
1. the First Derivative Test
2. the Second Derivative Test

Which have you been using in this problem?
Note that -1.2 E-6 is a very small number! You could regard that as close enough to 0.

Answer 2

I'm not sure, it's a problem for a lab on how to use the graphing calc. I'm using a ti-83 thats all i know haha

Answer 3

Everytime I've tried to do the minimum i've got an answer like that. Would i just say (0,1)?

Answer 4

I'll be right with you!

Answer 5

No hurry, thanks!

Answer 6

Would you mind explaining how you got the coordinates of the possible minimum?

Answer 7

I input the problem as Y1 then went to calculate the minimum and put my arrows on both sides of what I though the minimum is

Answer 8

I see: you're attempting to do this problem graphically. What level is this calculus course? high school? Adv placement? college?

Answer 9

It's math 95 intermediate algebra. We are just starting to use a graphing calc and that was one of the problems on our lab

Answer 10

So the emphasis seems to be on using a graphing calculator more (much more) than on Calculus per se?

Answer 11

I suppose? I'm not sure

Answer 12

don't want to waste your time! Have to be sure I understand where you're coming from.
I take it you haven't had calculus yet. (That's OK...plenty of time for that later). thus, we'll need to obtain our "answers" from the calculator, graphically. Are you using a TI-84, by any chance?

Answer 13

It's mainly just getting use to using the graphing calculator and I believe the answer can be approximate

Answer 14

ti-83

Answer 15

OK: have you been able to graph the given function? If so, do you see a max and a min in your graph?

Answer 16

for the max I got(2.631, 46.370) for min (1.4281 E-6, 1) I keep getting different but similar answers for the x minimum

Answer 17

I think it's to be expected that there'll be variation among your approx. answers. Nothing to worry about.

Are you using TRACE or the MINIMUM OR MAXIMUM command(s) to obtain your results?

Answer 18

I hit 2nd trace and then the min and max buttons

Answer 19

I'll be right with you!

Answer 20

ok!

Answer 21

You should get approx. the same answers using either tool. I have a TI-83 also. At this point, understanding that your answers probably will be approx. rather than exact, how can I help you further? (I'd be happy to do whatever I can.)

Answer 22

Can you just try it once and tell me if you're approx is similar to mine? Sorry I really want full points on this assignment! haha. I really appreciate your help

Answer 23

Certainly! Just a moment, please.

Answer 24

Thanks!

Answer 25

I get MINIMUM at (0,-1), having used the MINIMUM function, and

Answer 26

Where is the minimum function?

Answer 27

MAXIMUM at (1.106,0.103).

Do you have the function graphed, still?

Answer 28

Ya what settings do you have your window at? does that make a difference?

Answer 29

Oops. Looks like I typed in the function wrong: I typed in -1 instead of +1. That will certainly affect my answers.

It'l take just a moment to find the MINIMUM.

Answer 30

You were making me nervous haha

Answer 31

So sorry. Really!
MINIMUM AT (0,1).

Answer 32

No worries and the max the answer you put above or did you get the answer I have?

Answer 33

maximum at (0.887,3.259).

Answer 34

Now I'm going to guide you thru use of the MIN and MAX functions on your own calculator. Ready?

Answer 35

Yes

Answer 36

Assuming that you still have that graph visible:

Answer 37

I do

Answer 38

Press the 2nd key (it's yellow).
Then press the TRACE key (which says, in yello, CALCULATE). ok SO FAR?

Answer 39

got it

Answer 40

now press 3 to select MINIMUM.

Answer 41

ok

Answer 42

nOW YOUR calculator is asking you for the "left bound." simply move the cursor to the left of the minimum you see on your graph...that is, to the left of x=0.

Answer 43

Press enter.

Answer 44

Do the window settings make a difference in my answer?

Answer 45

So long as you can see the pertinent part of your graph, where the MIN and the MAX are, NO.

Answer 46

what are your settings just so I can see if its makes a difference I'm still getting the same answer

Answer 47

I set my window to display xmin = -1, xmax=2, xscl -1, and then adjust the y min and y max values so I can see the min and max of the graph displayed on my screen.

Answer 48

BRB. Bathroom break.

Answer 49

Okay

Answer 50

Want to proceed with the max, or would you like to re-do MIN?
takes only a few seconds.

Answer 51

I'm just not sure why I'm getting such different answers?

Answer 52

We'll go into that. No problem.
For now, let's redo the MIN, OK?

Answer 53

Ok

Answer 54

Display the graph. Press 2nd and then TRACE/CALCULATE.

Answer 55

ok

Answer 56

sEE THAT MENU? Just press 3 for min.
Use the arrow keys to position the cursor anywhere to the left of x=0.

Answer 57

done

Answer 58

press enter.
Move the cursor anywhere to the right of x=0 (because we see that the min is at or near x=0).

Answer 59

Ok

Answer 60

1.3389 E-6 and 1 is what I got

Answer 61

press enter.
Calculator will ask you, "GUESS?" type in anything you want that's close to 0: e. g., 0.1

Answer 62

calculator returns its value for x and y.

Your calculator returns x=?
and y=?

Answer 63

When I put in my guess it did show up x=0 and y=1. Usually I never put a guess?

Answer 64

You put in a "guess" of the x-value; if you chose 0, the calculator is confirming that x actually is 0 at the min.; if you chose x=0.1 for your guess, the calculator will find x=0 again. That's the beauty of it; you approximate things and the calc will give you a more accurate result.

Answer 65

Wow! good to know!

Answer 66

So you've found taht the minimum is at (0,1). Correct!!!

Answer 67

It only took me a couple days haha

Answer 68

You find the point that represents the MAX in the same way. Would you please experiment with that? I'll be back in a bout 5 minutes.

Answer 69

Of course, now you press the MAX key (#4), instead of the MIN key (#3).

Answer 70

Please excuse me; I'll be back.

Answer 71

Ok, thanks!

Answer 72

Have you tried finding the MAX on the calculator?
If not, here goes.

Answer 73

Ya I keep getting the same answer

Answer 74

And what answer is that?

x=
y=

Answer 75

x=2.6311201
y=46.369764

Answer 76

Very surprising. something's wrong here.
Would you please type here what expression you typed into your calculator for y= as you began to graph this function? Look at the calculator, not at the actual problem.

Answer 77

-x^5+3x^4+4x^2+1 is what I have typed in

Answer 78

I found I made another mistake: I typed in -5*x^5 instead of -x^5.
So, it may be that your result (the MAX) was right all along and I was the one who was wrong. Do you have any reason to doubt your own answer now?

Answer 79

No I thought it was correct until you showed me that I should be putting something in when it ask to guess. I thought because I hadn't guessed maybe I was getting that answer

Answer 80

I did a rough calculation and now have x=2.67, y=46.3, so it appeasrs that you were right all along! Congrats. And shame on me!

Answer 81

Have we left any stones unturned?

Answer 82

No worries you def helped me a lot. I really appreciate it!

Answer 83

You're awesome, thanks so much!

Answer 84

so happy to hear that! Do contact me personally if you have further questions. Thanks for your perseverance. Mind if I ask what state you're in and what grade?

Answer 85

I'm in Oregon and a sophomore at COCC community college

Answer 86

Cool. I'm in California and I was a college sophomore 1963-64. ( !! ) I'm a retired math prof.
So nice working with you. All the best to you. 'Til next time... bye MM

Answer 87

I'm from Santa Barbara! :) thanks!!!