# Thread: Show that there are no tangents to the curve y = (x+2)/(3x+4) with a positive slope.

1. ## Show that there are no tangents to the curve y = (x+2)/(3x+4) with a positive slope.

Show that there are no tangents to the curve $y=\frac{x+2}{3x+4}$ with a positive slope.

How would I solve this? All help appreciated!

2. Originally Posted by youngb11
Show that there are no tangents to the curve $y=\frac{x+2}{3x+4}$ with a positive slope.

How would I solve this? All help appreciated!
Calculate the numerator of the derivative with the Quotient Rule
and show that it cannot be >0

(the denominator of the derivative is a square)

$v\frac{du}{dx}-u\frac{dv}{dx}=(3x+4)-3(x+2)$

3. Originally Posted by Archie Meade
Calculate the numerator of the derivative with the Quotient Rule
and show that it cannot be >0

(the denominator of the derivative is a square)

$v\frac{du}{dx}-u\frac{dv}{dx}=(3x+4)-3(x+2)$
Numerator worked out to be $-2$. Any tips on how you would show it (format) if you were doing it? Thanks again!

4. The derivative gives you the slope of the tangent, in terms of x.
Since the denominator is a square, it's positive.
Then, since the numerator is free of x and negative, the derivative is always negative,
which means that all tangents have negative slopes
(no tangent has a positive slope).