Tangent and Normal Lines

Printable View

November 25th 2009, 10:49 PM
mj.alawami

Tangent and Normal Lines

Question:
Find the equation of the normal lines to the curve $y=x^4$ which is parallel to the line $2x+y=3$

Please answer in steps..
Thank you
November 25th 2009, 10:58 PM
Arturo_026

First you need to find the derivative:

$y' = 4x^3$

Then, from the equation of the line you are given, you see that the slopes of the normal line is -2 ; and since you want the slope of the tangets, you get the opposite reciprocal of -2, which is m=1/2.

Now you have y', just plug it in the derivative function and find your x.
Then with that, go back to the original equation and find y.
And you have all the ingredients necessary to set a line equation of the normals.
November 26th 2009, 12:53 AM
mj.alawami

Quote:

Originally Posted by Arturo_026

First you need to find the derivative:

$y' = 4x^3$

Then, from the equation of the line you are given, you see that the slopes of the normal line is -2 ; and since you want the slope of the tangets, you get the opposite reciprocal of -2, which is m=1/2.

Now you have y', just plug it in the derivative function and find your x.
Then with that, go back to the original equation and find y.
And you have all the ingredients necessary to set a line equation of the normals.

So From what i understood?

$4x^3=\frac{1}{2}$
$x=\frac{1}{2}$

$y-\frac{1}{16}=\frac{1}{2}(x-\frac{1}{2}$
$x-2y+\frac{3}{8}$

Is my answer correct??

If not please answer in steps
November 26th 2009, 02:11 AM
mathaddict

Quote:

Originally Posted by mj.alawami

So From what i understood?

$4x^3=\frac{1}{2}$
$x=\frac{1}{2}$

$y-\frac{1}{16}=\frac{1}{2}http://mathhelpforum.com/calculus/116799-tangent-normal-lines.html#post412400\$

So From what i understood?

$4x^3=\frac{1}{2}$
$x=\frac{1}{2}$

$y-\frac{1}{16}=\frac{1}{2}(x-\frac{1}{2}$
$x-2y+\frac{3}{8}$

Is my answer correct??

If not please answer in steps

Your answer is partly correct. You have the right values of $x$ and $y$ , but the wrong gradient. The gradient of the normal is $-2$ , so the equation is:

$y-\frac{1}{16}=-2\left(x - \frac12\right)$

i.e. $16y-1=-32x + 16$

i.e. $32x+16y-17 =0$
Grandad