# Derivative of function

• Oct 24th 2009, 07:43 PM
live_laugh_luv27
Derivative of function- tangent/normal
$y = \frac{3x+4}{x-1}$

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

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

Here are my answers..are they correct?

a. All real numbers not equal to 1

b. $\frac{-5}{(x-1)^2}$
• Oct 24th 2009, 07:46 PM
Prove It
Quote:

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

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

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

Here are my answers..are they correct?

a. All real numbers not equal to 1

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

a) Correct.

b) Incorrect. Should actually be $-\frac{7}{(x - 1)^2}$.
• Oct 25th 2009, 11:35 AM
live_laugh_luv27
ok, thanks.
• Oct 25th 2009, 11:38 AM
live_laugh_luv27
1) Find line tangent to the curve at $(8,4)$
2) Find line normal to the curve at $(8,4)$and determine the cooridinates of another point where this line intersects the graph.
1) $y-4=-\frac{7}{64}(x-8)$
2) $y-4=\frac{64}{7}(x-8)