Calculus

[Kaikai28]

Hello. How to find the equation of the horizontal and vertical tangents to the curve x^2+4xy+16y^2=27 I really need help. Pls

 

[Steven G]

You compute the derivative and for horizontal tangents you set the derivative = ? and for vertical tangents you set derivative = ?

What form is the equation of a horizontal line? How about a vertical line?

 

[Dr.Peterson]

Hello. How to find the equation of the horizontal and vertical tangents to the curve x^2+4xy+16y^2=27 I really need help. Pls

If your difficulty is in finding the derivative, do it implicitly. Then, of course, you'll be looking for where it is zero or undefined.

Please show us your work, so we can see what help you need. That's a lot more efficient than trying to guess what to focus on.

 

[Kaikai28]

I have not finished answering. This is my answer but I think its wrong.

 

[Dr.Peterson]

I have not finished answering. This is my answer but I think its wrong.

Thanks. That's exactly what we ask you to do:

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"Show work that you've already done (even if you think it's wrong), and try to explain why you're stuck."​

There's a lot of good work here. I do see a couple problem points.

One is that you write dy/dx = 0, but then find both where the numerator is 0 (good) and where the denominator is zero (that's an undefined derivative, not zero). So you've failed to distinguish the two kinds of points.

Then you took a solution that really has a horizontal tangent, called it vertical, and found the slope to be -1/5, which would be neither! Clearly that m should have been 0; you have a sign error.

Then you took a solution where the derivative is undefined and called it horizontal rather than vertical. You correctly found the derivative to be undefined; the next step will be to write the equation of that vertical line. What does the equation of a vertical line look like?

So the errors are small, though they look huge because of failing to pay attention to what horizontal and vertical mean.

 

[Kaikai28]

Thanks. That's exactly what we ask you to do:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...

www.freemathhelp.com

"Show work that you've already done (even if you think it's wrong), and try to explain why you're stuck."​

There's a lot of good work here. I do see a couple problem points.

One is that you write dy/dx = 0, but then find both where the numerator is 0 (good) and where the denominator is zero (that's an undefined derivative, not zero). So you've failed to distinguish the two kinds of points.

Then you took a solution that really has a horizontal tangent, called it vertical, and found the slope to be -1/5, which would be neither! Clearly that m should have been 0; you have a sign error.

Then you took a solution where the derivative is undefined and called it horizontal rather than vertical. You correctly found the derivative to be undefined; the next step will be to write the equation of that vertical line. What does the equation of a vertical line look like?

So the errors are small, though they look huge because of failing to pay attention to what horizontal and vertical mean.

Thanks. That's exactly what we ask you to do:

Posting Guidelines (Summary)

Welcome to our tutoring boards! :) This page summarizes the main points from our posting guidelines. As our name implies, we provide math help (primarily to students with homework). We do not generally post immediate answers or step-by-step solutions. We don't do your homework. We prefer to...

www.freemathhelp.com

"Show work that you've already done (even if you think it's wrong), and try to explain why you're stuck."​

There's a lot of good work here. I do see a couple problem points.

One is that you write dy/dx = 0, but then find both where the numerator is 0 (good) and where the denominator is zero (that's an undefined derivative, not zero). So you've failed to distinguish the two kinds of points.

Then you took a solution that really has a horizontal tangent, called it vertical, and found the slope to be -1/5, which would be neither! Clearly that m should have been 0; you have a sign error.

Then you took a solution where the derivative is undefined and called it horizontal rather than vertical. You correctly found the derivative to be undefined; the next step will be to write the equation of that vertical line. What does the equation of a vertical line look like?

So the errors are small, though they look huge because of failing to pay attention to what horizontal and vertical mean.

THANK YOU SO MUCH FOR YOUR HELP!

 

[Steven G]

The equation of a horizontal line is always in the form y = k, where k is some number.
The equation of a vertical line is always in the form x = k, where k is some number.

 

[Kaikai28]

[MATH] [QUOTE="Jomo, post: 519227, member: 46610"] The equation of a horizontal line is always in the form y = k, where k is some number. The equation of a vertical line is always in the form x = k, where k is some number. [/QUOTE] Thanks for your help. [/MATH]