There are multiple ways. One way is to plug in a slightly large angle and a slightly smaller angle and verify that the volume is smaller in both cases.
You can also take the second derivative and look for concavity. We have a playlist on how to determine max / min. CALCULUS 1 CH 7 SLOPE, CONCAVITY, MAX, MIN
Professor, why couldn't we use the equation, " S = R* (theta) " where S is the length of the arc which is basically " 2 * Pi * r " and then from that figure out "theta" ? Why am I getting a different result from this method from your method to figure out "theta" ?
Without seeing your work I cannot be sure where your error is, but as you can imagine, I have seen lots 's errors after having graded over 1000 tests. The error usually arises from a single logic error. The student writes something down that is not correct. Thus you need to go back to each step and determine if that step is logically and mathematically correct. The example in the video shows how to do the problem correctly.
Nope, S=R*(theta) is arc length of wedge and 2*pi*r is circumference of cone base circle. The two are irrelevent. *My greetings on the feet of the professor.*
could you explain biasing of a transistor , why need to bias it ? what are the formulas used for biasing a transistor and also does it add dc signal voltage with ac signal to amplify ac input by its current gain factor alpha ?
It's very nice. Afterwards one could ask students about continuity of V(h), and if V'(h) is defined everywhere in the optimization interval. Also the values at the endpoint should be checked.
Sometimes it makes more sense when you see numbers for the constants, instead of letters. But in the end, it is better to learn to manipulate the formulas and equations using letters and symbols, because it will help in the future.
I tried it with different values of big R and the value of little r as well as value of height ..h..changes .... hence the value of angle theta will also vary. Pls ignore my previous comment about a 66 degree constant theta.
You’re making one mistake at the end which is giving you the wrong answer, when you say what the circumference is equal to, but I will say this method is easier than taking a derivative of the entire volume equation with respect to theta. The answer should be pi(⅔)^(½), if you just say (R)theta=2pi(r)
Oh never mind, we just solved for inverse angles. I solved for 294 degrees which is the optimal angle for cone volume, and you solved for 66, which is the angle you’d have to cut out and throw aside. I take it back!
So is it correct to say that....theta will always be 66 degrees ..no matter what the initial big R value is ? (In regards to finding Max Vol of cone.)
an absolute legend... thank u...
Does anyone know how to verify that this is a maximum using derivatives?
There are multiple ways. One way is to plug in a slightly large angle and a slightly smaller angle and verify that the volume is smaller in both cases.
How would you do this with calculus?
You can also take the second derivative and look for concavity. We have a playlist on how to determine max / min. CALCULUS 1 CH 7 SLOPE, CONCAVITY, MAX, MIN
@@MichelvanBiezen yes, R^2 being constant vanishes and we are left with - sign term.
I bow thou for your effort.
Professor, why couldn't we use the equation, " S = R* (theta) " where S is the length of the arc which is basically " 2 * Pi * r " and then from that figure out "theta" ? Why am I getting a different result from this method from your method to figure out "theta" ?
Without seeing your work I cannot be sure where your error is, but as you can imagine, I have seen lots 's errors after having graded over 1000 tests. The error usually arises from a single logic error. The student writes something down that is not correct. Thus you need to go back to each step and determine if that step is logically and mathematically correct. The example in the video shows how to do the problem correctly.
Nope, S=R*(theta) is arc length of wedge and 2*pi*r is circumference of cone base circle. The two are irrelevent.
*My greetings on the feet of the professor.*
could you explain biasing of a transistor , why need to bias it ? what are the formulas used for biasing a transistor and also does it add dc signal voltage with ac signal to amplify ac input by its current gain factor alpha ?
It's very nice. Afterwards one could ask students about continuity of V(h), and if V'(h) is defined everywhere in the optimization interval. Also the values at the endpoint should be checked.
Good input.
Very nice explanation thx. How to calculate V(max) with teta ? What will be the expression of V(max) with teta ? Thank you 👍🏽
Our suggestion is to use the variables available. In this case the volume is expressed in terms of the variables shown in the video.
Amazing video and explanation! THANK YOU!!!!
Glad it was helpful! 🙂
You are a gifted professor.I think this prob would be easier for us to follow if you initially assigned a numerical value to Big R . Do you agree?
Sometimes it makes more sense when you see numbers for the constants, instead of letters. But in the end, it is better to learn to manipulate the formulas and equations using letters and symbols, because it will help in the future.
good point
@@MichelvanBiezen yes, you are pointing towards inherent generalisation which would have lost with fixed value of big R.
Such an amazing explanation, thank you so much
Thank you. Glad it helped. 🙂
I tried it with different values of big R and the value of little r as well as value of height ..h..changes .... hence the value of angle theta will also vary. Pls ignore my previous comment about a 66 degree constant theta.
I believe your previous comment was correct. No matter what R can be, r and height will change, but the theta to give max volume will always be 66.
What is the need of the angle sir??i didnt get it
Imagine you want to make this cone (the maximum volume cone) from a piece of paper. Then you need the angle to make it.
thank you, sir, it's be so easy and fun
Welcome!
but where is the calculus I mean differentiation?
Differentiation w.r.t. h and equating to zero. To find maxima.
very useful thank you
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Thank you. Glad you like our videos.
You’re making one mistake at the end which is giving you the wrong answer, when you say what the circumference is equal to, but I will say this method is easier than taking a derivative of the entire volume equation with respect to theta. The answer should be pi(⅔)^(½), if you just say (R)theta=2pi(r)
Oh never mind, we just solved for inverse angles. I solved for 294 degrees which is the optimal angle for cone volume, and you solved for 66, which is the angle you’d have to cut out and throw aside. I take it back!
Good input. Thanks for the comment.
Tough problem.
Oh yes it is.
i luv u biezen