Calculus AP problem, wrong answer in book?

Test Preparation AP Test Preparation
1

<p>Hey guys, just joined the site. I see you've got a nice section dedicated to the AP tests. Very cool.
Anyhow, I came accross this problem online and wanted to get the opinions of others on this board as to whether or not the answer key has given the wrong answer to this problem.</p>

<p>Q. Give the equation of the normal line to the graph of
y=3x(sqrt(x^2+6)+4
At the point (0,4)</p>

<p>I took the derivative and got (6x^2+18)/(sqrt(x^2+6))
substituted it into the form y-f(a)=f'(a)(x-a). Flipped it along with the sign (as it's the normal line, so its the reciprocal slope with the opposite sign) and got
y= -((sqrt(6))/(18))x +4</p>

<p>The book is giving the answer of x + 3(sqrt(6))y=12(sqrt(6)) </p>

<p>If any of you have the time to check this out, it would be greatly appreciated. The original equation can be found here -
<a href="http://online.math.uh.edu/apcalculus/exams/AP_AB_version1_2.htm%5B/url%5D"&gt;http://online.math.uh.edu/apcalculus/exams/AP_AB_version1_2.htm&lt;/a>
Problem 9</p>

<p>Once again, thank you.</p>

2

<p>Your answer and the book’s answers are the same.</p>

<p>x + (3√6)y = 12√6</p>

<p>(3√6)y = -x + 12√6</p>

<p>y = -x/(3√6) + 4 = -(√6/18)x + 4</p>

<p>Since the answer choices can only give you one equation for the line, you have to be able to quickly algebraically manipulate your answer to match one of the answer choices.</p>

3

<p>Wow, thank you very, very much for taking the time to look over that.</p>