tangency, optimization, and derivatives: just tell me solns

[crzymath]

im new to this forum and have some problems regarding tangency, optimiazation, and derivatives that i need some help on. i dont want someone to do the hwk! i just want a little guidance so i can start off the problem-im just stuck. please help. :?

1) show that the sum of the x and y intercepts of any tangent line to the curve sqrt x + sqrt y = sqrt c is equal to c.

i know i need to use the tangent line - but how?

2) show that the equation of the tangent line to the hyperbola (x^2 / a^2) - (y^2/ b^2) = 1 at (x[sub:3nylwj95]0[/sub:3nylwj95] and y[sub:3nylwj95]0[/sub:3nylwj95]) is [(x[sub:3nylwj95]0[/sub:3nylwj95]x) /( a^2)] - [(y[sub:3nylwj95]0[/sub:3nylwj95]y)/(b^2)] = 1

3) show using CALCULUS that all of the isoceles triangles with a given perimeter P, the one with the greatest area is equilateral (optimization problem)

thanks!
ps-please just tell me the right solution so i could compare to make sure i get it right! thanks again

 

[mmm4444bot]

Re: tangency, optimization, and derivatives-please HELP!!

... please just tell me the right solution so i could compare to make sure i get it right!

Hello Crazy M:

You've got it backwards.

You show us your solution, first. Then we will tell you whether or not it is correct.

Here is my boilerplate response, for you, as well.

At the top of this board's index, you will find a post titled, "Read Before Posting".

Please, read it.

It outlines your responsibilities for seeking help at this web site.

The main points of that post are (1) we don't simply guess at lessons which we could type for you to provide solutions for your homework, and (2) you make it very difficult for people to help you when you withhold your knowledge and attempts.

After you read your responsibilities, then please come back and show us what you've been able to accomplish so far on these exercises. It would be even better if you could also include statements about why you're stuck.

We are eager to help guide you.

Cheers,

~ Mark



"Spoon feeding, in the long run, teaches us nothing but the shape of the spoon" -- E.M. Forster

 

[mmm4444bot]

Re: tangency, optimization, and derivatives-please HELP!!

... i just want a little guidance so i can start off the problem-im just stuck ...

Oh, on the offhand chance that you just blew your stack, I post more.

At what point are you stuck? If you're in calculus, then you must have learned something along the way. I do not believe that you have absolutely nothing to say about these exercises.

"It is a waste of my personal time to type a bunch of stuff that people already know." -- Yours Truly

 

[galactus]

3) show using CALCULUS that all of the isosceles triangles with a given perimeter P, the one with the greatest area is equilateral (optimization problem)

Let a=the length of the two equal sides. Let h= the height of the triangle.

Let p=the perimeter.

Therefore, the base is \(\displaystyle p-2a\)

\(\displaystyle h^{2}=a^{2}-\left(\frac{p-2a}{2}\right)^{2}\)

\(\displaystyle A=\frac{1}{2}h(p-2a)\)

Sub in h, differentiate and solve for a. You should get a=p/3 if done correctly.

 

[Deleted member 4993]

im new to this forum and have some problems regarding tangency, optimiazation, and derivatives that i need some help on. i dont want someone to do the hwk! i just want a little guidance so i can start off the problem-im just stuck. please help. :?

1) show that the sum of the x and y intercepts of any tangent line to the curve sqrt x + sqrt y = sqrt c is equal to c.

i know i need to use the tangent line - but how?

You know the slope of the tangent line (dy/dx), you know a point it passes through (the point of tangency on the curve) - find the equation of the line and the intercepts and add those up.

2) show that the equation of the tangent line to the hyperbola (x^2 / a^2) - (y^2/ b^2) = 1 at (x[sub:3kwd8q51]0[/sub:3kwd8q51] and y[sub:3kwd8q51]0[/sub:3kwd8q51]) is [(x[sub:3kwd8q51]0[/sub:3kwd8q51]x) /( a^2)] - [(y[sub:3kwd8q51]0[/sub:3kwd8q51]y)/(b^2)] = 1

It is similar to above.

3) show using CALCULUS that all of the isoceles triangles with a given perimeter P, the one with the greatest area is equilateral (optimization problem)

thanks!
ps-please just tell me the right solution so i could compare to make sure i get it right! thanks again