Show that there are no tangents to the curve $\displaystyle y=\frac{x+2}{3x+4}$ with a positive slope.
How would I solve this? All help appreciated!
Show that there are no tangents to the curve $\displaystyle y=\frac{x+2}{3x+4}$ with a positive slope.
How would I solve this? All help appreciated!
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).