# Adv. Functions: Rate of Change in Rational Functions

1. Sep 29, 2014

### harujina

1. The problem statement, all variables and given/known data
mtan for f(x) = 5/√ 3x ... at x=1

2. Relevant equations
msec = y2-y1 / x2-x1

3. The attempt at a solution
The two points I got from the equation: (1, 5/√ 3) and (1+h, 5/√ 3+h)

msec = f(1+h) - f(1) / h
= (5/√ 3+h - 5/√ 3) / h ... multiply top and bottom by denominators (√ 3+h) and (√ 3)
= 5√ 3 - 5√ 3+h / h(√ 3+h)(√ 3) ... multiply top and bottom by the conjugate (5√ 3 + 5√ 3+h)
= 25√ 9 + 25√ 9+h - 25√ 9+h - 25√ 9+h2 / h(√ 3+h)(√ 3)(5√ 3+5√ 3+h)
= 25√ 9 - 25√ 9+h2 / h(√ 9+h)(5√ 3+5√ 3+h)
= 75 - 25√ 9+h2 / h(5√ 27+3h + 5√ 27+3h2)

No idea if this is right and where I'm going with this.
I don't know the answer to this question either, so can't check my work...

2. Sep 29, 2014

### Staff: Mentor

Please clarify what you're saying here. Which if these is your function?
$$1. f(x) = \frac{5}{\sqrt{3}}x$$
$$2. f(x) = \frac{5}{\sqrt{3x}}$$
$$3. f(x) = \frac{5}{\sqrt{3}x}$$

3. Sep 29, 2014

### harujina

Oh, the second one.
$$2. f(x) = \frac{5}{\sqrt{3x}}$$

4. Sep 29, 2014

### Staff: Mentor

You need more parentheses.
The second point should be written as (1 + h, 5/√(3 + h)), otherwise the 2nd coordinate looks like this:
$$\frac{5}{\sqrt{3}} + h$$
The right side should be written as (f(1 + h) - f(1))/h. Most would interpret what you wrote as
$$f(1 + h) - \frac{f(1)}{h}$$
You have the right idea, but with all the missing parentheses, it's just too hard to read.

5. Sep 29, 2014

### Staff: Mentor

When it's completely simplified, you should get this:
$$\frac{-5\sqrt{3}}{6}$$

BTW, LaTeX makes it much easier to read, and isn't that hard to write.
To create a fraction, do this:
Code (Text):
\frac{a + b}{c}
I don't show the pairs of $symbols at front and back. This renders like so: $$\frac{a + b}{c}$$ To create a square root, do this: Code (Text): \sqrt{3 + h} Again, you need$ pairs at front and back.
This is how it looks in the browser:
$$\sqrt{3 + h}$$

Last edited: Sep 29, 2014