line that is tangent to a curve ata particular point

Find the line that is tangent to the curve with the function y^2=x+3 at point (6,-3)

I know m=dy/dx so implicit derivative is: 2y dy/dx=1, so dy/dx = 1/2y

then equation of a line y-y_1=m(x-x_1). thus y+3=1/2y(x-6)

I can't believe that this is suppose to be my answer as this is clearly not a straight line. What am I doing wrong?

Thanks

Re: line that is tangent to a curve ata particular point

Quote:

Originally Posted by

**Bowlbase** Find the line that is tangent to the curve with the function y^2=x+3 at point (6,-3)

I know m=dy/dx so implicit derivative is: 2y dy/dx=1, so dy/dx = 1/2y

then equation of a line y-y_1=m(x-x_1). thus y+3=1/2y(x-6)

I can't believe that this is suppose to be my answer as this is clearly not a straight line. What am I doing wrong?

At the point $\displaystyle (6,-3)$ we have $\displaystyle \frac{dy}{dx}=\frac{-1}{6}$.

Re: line that is tangent to a curve ata particular point

Really, that simple? Geez..

Thanks

Re: line that is tangent to a curve ata particular point

Rather than make a new thread I have similar question as before but no points given

Find all the lines tangent to the curve y=x^3 and is parallel to y=3x-5.

I have that the slope must be the same as the given line, so m=3. The derivative of the curve also gives slope so 3x^2=3 where x is +-1.

So I have only 1 point to find in my line equation. I have y-y_1=3(x+-1). I'm stuck on trying to figure out what y_1 is here.

Pretty sure this is going to be another oh geez moment. Thanks for the help.

Re: line that is tangent to a curve ata particular point

Quote:

Originally Posted by

**Bowlbase** Rather than make a new thread I have similar question as before but no points given

Find all the lines tangent to the curve y=x^3 and is parallel to y=3x-5.

I have that the slope must be the same as the given line, so m=3. The derivative of the curve also gives slope so 3x^2=3 where x is +-1.

So I have only 1 point to find in my line equation. I have y-y_1=3(x+-1). I'm stuck on trying to figure out what y_1 is here.

**Always, always start a new thread for a new question!**

You have two points of tangency $\displaystyle ((1,1)~\&~(-1,-1)$

So you have two tangent lines.

Re: line that is tangent to a curve ata particular point

Sorry, I'll make a new thread next time.

So I understand that there will be two lines but I don't see where the y values are coming from. I am assuming that you just put the x values into the y=x^3. Is this correct?

Re: line that is tangent to a curve ata particular point

Quote:

Originally Posted by

**Bowlbase** So I understand that there will be two lines but I don't see where the y values are coming from. I am assuming that you just put the x values into the y=x^3. Is this correct?

since the tangent line "touches" the curve at the point of tangency, that would be correct.

Re: line that is tangent to a curve ata particular point

makes perfect sense, thank you.