Does my solutions correct? I someone to check.

[duffymercy]

I need someone to check my solutions if they are correct. And i need help about how to find normal equation of curve.(last picture)

Thanks for your time.

 

[HOI]

It's almost impossible to read those! Couldn't you type them in? For that matter why couldn't you check the answers yourself?

 

[duffymercy]

It's almost impossible to read those! Couldn't you type them in? For that matter why couldn't you check the answers yourself?

I don't know how to type them in pc, and i have bionic hand that's why i can't write good. Sorry.

 

[anemone]

Hi duffymercy, if you don't know how to type math expression/equation in $\LaTeX$, perhaps you want to check this https://mathhelpboards.com/threads/mhb-latex-guide-pdf.1142/ out. (Smile)

But, if you want to upload the picture of the math problem and your solution to the problem here so we could see if you have got a sound solution, you could help us out by uploading a picture that is visible to us, okay?(Nod)

 

[duffymercy]

I hope it's better

Hi duffymercy, if you don't know how to type math expression/equation in $\LaTeX$, perhaps you want to check this https://mathhelpboards.com/threads/mhb-latex-guide-pdf.1142/ out. (Smile)

But, if you want to upload the picture of the math problem and your solution to the problem here so we could see if you have got a sound solution, you could help us out by uploading a picture that is visible to us, okay?(Nod)

In the first picture we are looking for inflection point and concavity.
In the second picture we are looking for max volume of cone. We have hypotenuse value.

https://www.physicsforums.com/attachments/311841._xfImporthttps://www.physicsforums.com/attachments/311842._xfImporthttps://www.physicsforums.com/attachments/311843._xfImport

 

[anemone]

Can you post the question as well because without the question, it is hard for us to know what you are trying to solve...

 

[duffymercy]

Can you post the question as well because without the question, it is hard for us to know what you are trying to solve...

In the first picture we are looking for inflection point and concavity of the curve.
In the second picture we are looking for max volume of cone that generated by right triangle rotated about one of it's legs. We have the hypotenuse value.
Third picture explains itself.

 

[skeeter]

inflection point is correct, as is concavity for signs shown for $f''$

max volume is ok ... I would have used $V = \dfrac{\pi}{3}(7h-h^3)$ instead of the trig functions

inverse derivative value is correct

 

[duffymercy]

inflection point is correct, as is concavity for signs shown for $f''$

max volume is ok ... I would have used $V = \dfrac{\pi}{3}(7h-h^3)$ instead of the trig functions

inverse derivative value is correct

Thank you so much, I learned $$V=(π/3)*r^2\sqrt(7−r^2)\ $$ method after I post it here. But still I think trig functions was easier. This method is more complicated.

 

[duffymercy]

inflection point is correct, as is concavity for signs shown for $f''$

max volume is ok ... I would have used $V = \dfrac{\pi}{3}(7h-h^3)$ instead of the trig functions

inverse derivative value is correct

AH LOL, I just saw what you did there, if I would've do it for h instead of r, taking derivative could be easier...
work smart ... not hard. it explains everything...