Critical points, local max/min hw help please!

[danielCho]

Hi, can someone help me with how to do this hw? I tried to do it the best I could but I only got so far, this is calc one.

#18 graph. It states to just find the local min/max and absolute min/max


#30/#32


#38/#44


Here's what I got so far the pink is the problem and green is my answer.





#30 I got some points but the critical point isnt correct I think.. On my math lab they get a + and a - such as +/- 4 while every single time I do it I get one point.

#32 I'm lost on how to figure out part b, would I just graph it and look from there?

#38 I get the critical point at -1 which doesn't seem right. I plug in -8 and 8 into the derivative function and from there I dont know which one to graph...

#44 I'm lost on how to plug ion the point [0,5]. I have two seperate functions which are e^(-x/2) and ((-x/2)+1). Or do I plug in the answers into the whole thing? Which is e^(-x/2)((-x/2)+1). And for part C i still dont know which one to graph to compare...

Any help is greatly appreciated.

 

[stapel]

30. You might want to review how to solve equations by taking square roots. For instance, since x² - 1 = (x - 1)(x + 1), shouldn't x² - 1 = 0 have two solutions?

32. The actual exercise is not displayed in the graphic. The instructions for the exercise set refer to "on the interval" but your homework shows "on the point", which I don't understand. Please reply with clarification.

38. On what basis have you concluded that your critical point is incorrect? Why are you plotting only at the endpoints of the interval? Why are you unfamiliar with how to find absolute max/min values on intervals? (Are you working ahead, and the class hasn't yet covered that chaper?)

44. Why are you thinking that the interval is a point? (Were you placed in calculus without having first taken the necessary algebra prerequisites, which would have covered this sort of material?)

Please be complete. Thank you!

 

[danielCho]

30. You might want to review how to solve equations by taking square roots. For instance, since x² - 1 = (x - 1)(x + 1), shouldn't x² - 1 = 0 have two solutions?

32. The actual exercise is not displayed in the graphic. The instructions for the exercise set refer to "on the interval" but your homework shows "on the point", which I don't understand. Please reply with clarification.

38. On what basis have you concluded that your critical point is incorrect? Why are you plotting only at the endpoints of the interval? Why are you unfamiliar with how to find absolute max/min values on intervals? (Are you working ahead, and the class hasn't yet covered that chaper?)

44. Why are you thinking that the interval is a point? (Were you placed in calculus without having first taken the necessary algebra prerequisites, which would have covered this sort of material?)

Please be complete. Thank you!

I wouldn't rather say this but my teacher is not up to par.. She doesn't seem to be able to teach our class which leaves us all in the "dark". Our recitation class has 35 students but when the instructor comes 80% of the class leaves just because there fed up with her... I've been trying to complete the homework she has given us with some students but it seems were all struggling.

And THANK YOU! That makes so much sense about how you get the two +/- points. So apparently when there is a perfect square we take the +/- of the number correct? I was doing the hw with my tutor and he couldn't really figure it out and just told me that there was one critical point! I'm still curious about how many critical points you know are there... I've just been basing it off the parent graph as a parabola will have only one critical point.

#38). I was thinking that the point is incorrect as in the MyMathLab problems skip that particular step but end up with two points as in +/-1 while I only ended up with -1.

#44). How the tutor explained interval point was the point x plugged into the function. From that my tutor said to take that number to find the absolute min/max!

Highest math class I ever took was college algebra a while ago.. I've been putting a lot of effort into this but its just hard because I wish my instructor would teach and that my tutor would teach correct methods because apparently hes been wrong a LOT ):

 

[stapel]

I wouldn't rather say this but my teacher is not up to par.

That may be so (and I've had similar experiences, so I'm not doubting you), but a big part of the issue seems to be your lack of familiarity with algebra, which you say you last saw "a while ago". One simply cannot succeed in calculus if one is shaky on the algebra.

So apparently when there is a perfect square we take the +/- of the number correct?

The side opposite the squared-variable term does not need to be a perfect square. Try studying the lesson at the link, provided earlier. This will help you understand what is going on, and how to deal with exercises for which the other side is not a perfect square.

...my tutor...just told me that there was one critical point!

For which exercise?

#38). I was thinking that the point is incorrect as in the MyMathLab problems skip that particular step...

Which "step"?

...but end up with two points as in +/-1 while I only ended up with -1.

Do you perhaps mean that "two x-values, rather than just one"? Because "+/-1" is two x-value; a "point" would be something like "(-1, 6)".

#44). How the tutor explained interval point was....

Okay; I don't think there is any such animal as an "interval point". Are you maybe referring to the "interval endpoints"? And maybe to plugging the x-values into the original function when checking for absolute max/min points on that interval? And then remembering to compare these values against the local max/min points found from critical points, so you can tell which is largest/smallest, which may not include an endpoint?

 

[danielCho]

That may be so (and I've had similar experiences, so I'm not doubting you), but a big part of the issue seems to be your lack of familiarity with algebra, which you say you last saw "a while ago". One simply cannot succeed in calculus if one is shaky on the algebra.

So apparently when there is a perfect square we take the +/- of the number correct?[/quoe]
The side opposite the squared-variable term does not need to be a perfect square. Try studying the lesson at the link, provided earlier. This will help you understand what is going on, and how to deal with exercises for which the other side is not a perfect square.


For which exercise?


Which "step"?


Do you perhaps mean that "two x-values, rather than just one"? Because "+/-1" is two x-value; a "point" would be something like "(-1, 6)".


Okay; I don't think there is any such animal as an "interval point". Are you maybe referring to the "interval endpoints"? And maybe to plugging the x-values into the original function when checking for absolute max/min points on that interval? And then remembering to compare these values against the local max/min points found from critical points, so you can tell which is largest/smallest, which may not include an endpoint?

I got some more clarification about the interval point. It seems you just plug in the interval points into the original equation and from there you have your domain! Well that's what my teacher said haha. Then once you have the domain and the critical points in the equation you compare and then you have your abs min/max values! I think I got most everything correct now. thanks for your help

 

[stapel]

I got some more clarification about the interval point. It seems you just plug in the interval points into the original equation....

The fact that you still think there is such a thing as an "interval point" suggests that, no, clarification has not been achieved. There are intervals, there are points, there are interval endpoints. There are no "interval points". And if you think that all max/min exercises are solved by plugging "interval points into the original equation", then I fear that the results on your next test are going to be disappointing.

Seriously, please talk to a qualified local tutor!