Can someone help me with optimization... (calc 1)

can someone help me with optimization... (calc 1)

i always go wrong somewhere

first problem. no idea how to simplify the surface area equation after plugging in

second problem. i get ridiculously high numbers for radius and area

blump

pls

will exchange for chemsitry knowledge for i know all

Your answer is google

You have to optimize with respect to two variables, h and r.
look at it this way: you have a constraint with a fixed V. This provides you with a relationship between r and h. You can use this to transform your problem into an optimization problem with only 1 variable.

For example: h=3V/pir^2

Now you can use that in A to only express A as a function of h.
The only thing you have to do is use the usual differentiation to find the optimal value of h, and finding the optimal value of A using that h.

Sounds good? You can do it.

Weird. I found that the optimal ratio r/h is sqrt(2), no matter what size.

Wow that second problem was fun to do. In all calculus optimization problems you'll have several variables which are related to each other, and you simplify an equation (for problem 7, for example, it's the Area equation) so that there are only two variables (Area and the length of a side, or the length of the semicircle, or even the diameter of the semicircle), take the derivative, set equal to zero, and that's your answer. An endpoint can also be your answer in rare cases, so make sure not to forget that.

Hated these problems in calc 1. Skipped them on every test. How does one study for these problems? When I took the class, the homework and test problems were completely different types of set up and stuff. Like unless you've seen the same exact problem before, there's no way you'd get it.

Is this true?

Do people seriously find these questions hard? Lol what the hell. Calc 1 is a joke

>AP Calculus AB
>never seen these problems before
>teacher gives us online hw
>Subject is optimization
>full of these problems
>don't know what to do
>look up solutions for 2~3 of these problems
>every other problem is similar
>can now do these problems

It's the same process, different formulas.

A=P^2/8π orisit?

You can solve it using the Lagrange multiplier method (of minimization / optimization), but I don't think it's taught in calc 1 since I used partial derivatives.

same here

If P is perimeter then your question makes no sense. Since the perimeter is always 1000m, that would make the area always the same, which is absolutely not true.

If anyone cares, here's the Lagrange multiplier method.

Never seen that before, but it seems like a super easy way to solve this, though not for AP calculus because partial derivatives are scary. I wish they taught us Lagrange multipliers and other convenient stuff (like Laplace transforms/Fourier transforms) in math like they did engineers. At best I saw that stuff my last year.

number 2

I'm pretty glad I learned this stuff. Our professor threw in the Lagrange optimization part even though it wasn't part of the curriculum because he thought it was cool.

A = maximum possible area of the rectangle given perimeter P.

Standard method, same result
I prefer general solutions
here a,b,A as functions of P

OP here, got the second one while i was at school, and thanks for help on the first one!

that was props for u!!

Very good. How does your paper cone look like?

Hopefully well optimized.