Average Value Theorem, Limits, and Slopes.

[ardentmed]

Hey guys,

I have a couple more questions about this problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help.

Question:

So for the first one, I just used f(b)-f(a)/ b-a and got 589, 1208, and 1366 respectively via simple substitution.

For 1b, I overaged the values from II and III and got 1287 stores/year.

As for c, I sketched the slope and got a line of best fit. Then I calculated the slope as 5886-1886 / 2002-1998 and got 1000 shops/year. But I'm not too sure about this answer. Are there better ways to compute the slope? As for 2a, I took sample values approaching 9, so x=9.1, .. x=9.0001 and ultimately guessed that the limit is 4.5.

As for b, I couldn't get a definitive answer, but I'm guessing that factoring works. Am I close?
Thanks in advance.

 

[MarkFL]

1a) i is incorrect, but I agree with the rest. b) Correct. c) You are asked to find the slope of a tangent, so you need a curve...

2.) The image is too dim for me to easily read. I suggest you create a new thread and either obtain a better image or preferably type the problem.

When your problems have multiple parts, it is best to create a separate thread for each.

 

[ardentmed]

1a) i is incorrect, but I agree with the rest. b) Correct. c) You are asked to find the slope of a tangent, so you need a curve...

2.) The image is too dim for me to easily read. I suggest you create a new thread and either obtain a better image or preferably type the problem.

When your problems have multiple parts, it is best to create a separate thread for each.

I re-did 1a i and ended up getting 1193 stores/year because:

(5886-3501) / (2002-2000) = 2385/2

~1192.5

 

[MarkFL]

I re-did 1a i and ended up getting 1193 stores/year because:

(5886-3501) / (2002-2000) = 2385/2

~1192.5

Looks good. :D