# Derivative of function

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• Oct 24th 2009, 06:43 PM
live_laugh_luv27
Derivative of function- tangent/normal
$\displaystyle y = \frac{3x+4}{x-1}$

a. Determine all values for $\displaystyle x$ for which $\displaystyle \frac{dy}{dx}$ exists.

b. Find an expression for $\displaystyle \frac{dy}{dx}$.

Here are my answers..are they correct?

a. All real numbers not equal to 1

b. $\displaystyle \frac{-5}{(x-1)^2}$
• Oct 24th 2009, 06:46 PM
Prove It
Quote:

Originally Posted by live_laugh_luv27
$\displaystyle y = \frac{3x+4}{x-1}$

a. Determine all values for $\displaystyle x$ for which $\displaystyle \frac{dy}{dx}$ exists.

b. Find an expression for $\displaystyle \frac{dy}{dx}$.

Here are my answers..are they correct?

a. All real numbers not equal to 1

b. $\displaystyle \frac{-5}{(x-1)^2}$

a) Correct.

b) Incorrect. Should actually be $\displaystyle -\frac{7}{(x - 1)^2}$.
• Oct 25th 2009, 10:35 AM
live_laugh_luv27
ok, thanks.
• Oct 25th 2009, 10:38 AM
live_laugh_luv27
2 additional questions:

1) Find line tangent to the curve at $\displaystyle (8,4)$

2) Find line normal to the curve at $\displaystyle (8,4)$and determine the cooridinates of another point where this line intersects the graph.

Here is what I came up with:

1) $\displaystyle y-4=-\frac{7}{64}(x-8)$

2) $\displaystyle y-4=\frac{64}{7}(x-8)$
Is this correct? I'm unsure what the second part of the second question is asking. Any help is appreciated.