How do you find the slope of the line normal to the curve (x^2+4)*y=8?


The normal line is perpendicular to the tangent line, meaning that it will have the opposite reciprocal slope of the tangent line. We use the derivative to give us the slope of the tangent line.

Don't use plagiarized sources. Get Your Custom Essay on
How do you find the slope of the line normal to the curve (x^2+4)*y=8?
Just from $13/Page
Order Essay

1) Find the derivative:

The function ##(x^2+4)*y=8## is written implicitly. We could therefore use to find the derivative. However, it is fairly simple to solve the function for y explicitly, which avoids the need for implicit differentiation. We shall take that approach.

Divide both sides of the equation by ##(x^2+4)## and we obtain the equation:

##y = 8/(x^2+4)## which is equivalent to ##y= 8*(x^2+4)^(-1)##. We can now use the to differentiate.

##y’=-1(x^2+4)^(-2)*2x## or ##y’=(-2x)/(x^2+4)^2##.

2) Find the slope of the tangent line.

At whatever given point (for example, x= 2) we wished to find the slope of the normal line, we would begin by finding the slope of the tangent line.

Using x=2 as our example, ##y'(2)=(-2*2)/(2^2+4)^2 = -4/8^2 =-4/64=-1/16##.

3) Find the slope of the normal line.

Since the slope of the tangent line at x=2 is ##-1/16##, the slope of the normal line would be the opposite reciprocal of this number or 16.

The same procedure could now be used for any other constant.

Show more


Source link

Place your order
(550 words)

Approximate price: $22

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
The price is based on these factors:
Academic level
Number of pages
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more

Order your essay today and save 15% with the discount code BANANA