Question:

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

Please answer in steps..

Thank you

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- Nov 25th 2009, 10:49 PMmj.alawamiTangent and Normal Lines
Question:

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

Please answer in steps..

Thank you - Nov 25th 2009, 10:58 PMArturo_026
First you need to find the derivative:

$\displaystyle y' = 4x^3$

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. - Nov 26th 2009, 12:53 AMmj.alawami
- Nov 26th 2009, 02:11 AMmathaddict
- Nov 26th 2009, 02:38 AMGrandad
Hello mj.alawamiYour answer is partly correct. You have the right values of $\displaystyle x$ and $\displaystyle y$, but the wrong gradient. The gradient of the normal is $\displaystyle -2$, so the equation is:

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

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

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