[Calculus] Limit/Derivative/Optimization; Check my Work Plz

Hello, I've been assigned a few calculus problems and I've completed 2 out of the 4 of them so far. I was wondering if anyone would be willing to check the first two, and if they have time, also offer me some insight on how to solve the second two?


Here is a link to my work: https://www.dropbox.com/s/jn0mqvt1gw4ttpp/calcProblems.pdf?dl=0
At the link is a seven-page document containing twelve exercises, some of which appear to have worked solutions provided. I can't speak for others, but I'm not going to print out the document, review all the exercises, and reply with solutions for all of them. :shock:

Kindly please reply with specifications regarding the two solutions you want checked, and the two others for which you need hints getting started. It would be very helpful if you posted the information here. Thank you! ;)
 
Hello, I've been assigned a few calculus problems and I've completed 2 out of the 4 of them so far. I was wondering if anyone would be willing to check the first two, and if they have time, also offer me some insight on how to solve the second two?


Here is a link to my work: https://www.dropbox.com/s/jn0mqvt1gw4ttpp/calcProblems.pdf?dl=0

I agree with staple. You should at least provide the particular problems you would like checked and the ones you are having trouble with.

Before I noticed the length of the document, I did look at Problem 2 (CORE), part one which ends
y = f'(a) (x-a) + f(a)
y= 13 (x+2) - 2
From the definition, what is a, f(a), and f'(a) and how does that compare to what is in the reset of the exercise?
 
@Ishuda:

The formula y = f'(a) (x-a) + f(a) appears to be the formula zimmertr was given for the tangent line to a function at the point x=a.


@Zimmertr

Your work on Problem 2 is mostly fine, but in the very last step your signs are reversed. You are plugged in a=-2 to the formula rather than a=2.

For problem 5, I see only one error. When taking the derivative of s(t), you use the quotient rule and end up (2t)2 in the denominator. You replace that with 22t in the next step, but that's not an equivalent value. 22t is actually (22)t or 4t. When dividing by 2t later on, however, you end up with the correct denominator.

For problem 10, I'm not 100% sure where you're having trouble. It seems to me a problem that involves simply knowing and using the definitions of various terms. For instance, in part one: What are the critical points of a function, and how do you find them? If you're stuck on specific parts, reply back and we can help you further.

For problem 12's first part, start by establishing what you know. You know that the gardens share one side, and that they're the same size. You know the perimeter is 200 square feet. If you call the length L and the width W, can you create a formula for the perimeter of the two gardens? And can you create a formula for the area of the gardens? Given those two formulas, solve for L in terms of W (or vice versa) and then maximize the perimeter formula.

And finally, the second part of problem 12 is same type of problem as problem 2 from your last thread. So, you can use the same strategy you used before, and you should be fine.
 
@Ishuda:

The formula y = f'(a) (x-a) + f(a) appears to be the formula zimmertr was given for the tangent line to a function at the point x=a.

...
Thanks. Yes, I was familiar with the formula y = f'(a) (x-a) + f(a), it is the result obtained that I was questioning. If one uses the a, f(a), and f'(a) from the problem as given one does not end up with the formula presented
y= 13 (x+2) - 2
 
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