Calc Application Sac Question

[Cosec]

Just two questions regarding a 3 day sac im currentely doing for Calc.

If a question gives a function, which shows the temperature of a incubator in terms of time, and it wants to know when the great rate of change of the temperature is. Would i be right in finding the derivative, graphing it, and then finding the maximum of the derivative graph? Which will give me the greatest gradient, which in this case is the greatest rate of change in the temp in terms of time?

And secondly, attached a picture is for a question.
Imgur: http://imgur.com/ESSumEE

Background: The questions is of a nusery owner, and provides a function for the number of plants in terms of time (months). The nusery owners assitant accidentely sprayed some of the plants with a weed killer so something, and so the new function of the number of plants is given. It asks us to find the value of 'a', which is a variable in the new function, and tells us to find it by letting the two functions equal each other and solve for a. This is the point from their on with regards time, that the new function is valid, and prior to this the old function is valid.

The question its self asks, what is the number of plants lost?
Their have been several answers from other people in the class. But I believe that you take the point at which a=, find the number of plants there, then subtract that from the minimum of the newer function. Another said that use just pick to points, and compare what the old function would of been, to the new function and calculate the difference and thats how much they have lost?
 
The question doesnt given any value of time, so its pretty broad. Any ideas?

[wunderkind52]

Just two questions regarding a 3 day sac im currentely doing for Calc.

If a question gives a function, which shows the temperature of a incubator in terms of time, and it wants to know when the great rate of change of the temperature is. Would i be right in finding the derivative, graphing it, and then finding the maximum of the derivative graph? Which will give me the greatest gradient, which in this case is the greatest rate of change in the temp in terms of time?

And secondly, attached a picture is for a question.
Imgur: http://imgur.com/ESSumEE

Background: The questions is of a nusery owner, and provides a function for the number of plants in terms of time (months). The nusery owners assitant accidentely sprayed some of the plants with a weed killer so something, and so the new function of the number of plants is given. It asks us to find the value of 'a', which is a variable in the new function, and tells us to find it by letting the two functions equal each other and solve for a. This is the point from their on with regards time, that the new function is valid, and prior to this the old function is valid.

The question its self asks, what is the number of plants lost?
Their have been several answers from other people in the class. But I believe that you take the point at which a=, find the number of plants there, then subtract that from the minimum of the newer function. Another said that use just pick to points, and compare what the old function would of been, to the new function and calculate the difference and thats how much they have lost?
 
The question doesnt given any value of time, so its pretty broad. Any ideas?

Check your pm!

[Apink!]

Woah! Doing a Calc. SAC already?
Mine's like in three weeks!
Good luck!

EDIT: Wunderkind, I was wondering if you could send me a PM on the answers to these as well. I haven't started the SAC yet, but I'm interested in how to solve these as well. Thanks!

[Cosec]

Woah! Doing a Calc. SAC already?
Mine's like in three weeks!
Good luck!

EDIT: Wunderkind, I was wondering if you could send me a PM on the answers to these as well. I haven't started the SAC yet, but I'm interested in how to solve these as well. Thanks!

Yeah, he wanted it done by the end of the semester. However, he has skipped a fair bit of stuff the class hasnt learned. But i do my own thing so im not really effected. Ill be more than happy to send you the sac im doing now once it gets marked and uploaded on to the network. Its pretty easy. For revision, i just did the chapter review of essentials worked problems close to 4 times, over a period of a month or so, so i forgot the questions. And spammed as many practice exams for their application questions so i could basically get an idea of every type of question possible.

[Cosec]

Anyone with regards the first question?
Second one has been sorted out.

[Tyleralp1]

Yeah, if you're able to share it please do so! I would love to see this.

[dankfrank420]

Just spitballing here for the first one, disregard if I'm wrong:

Don't you derive the derivative and let this second derivative equal 0? Essentially you want to derive the original function twice.

This way, you find the maximum value of the derivative (when gradient is highest) and hence the corresponding x-value?

[Apink!]

I thought that for the first one, you just find the derivative function and find the absolute maximum value on the graph.
(I think you are right Cosec)

But, you know  I might be wrong...

btw thanks! Uploading the SAC you did (as long as you don't mind it) would be very helpful for me (:

[keltingmeith]

I would like to remind people that the SAC is copyright material and so should not be uploaded to AN.