# How do you find the local extrema for  f(x) = (3x + 4)^(-3/4) ?

Jan 5, 2017

There are no specific values as local/global extrema.
Continuously f $\downarrow$, from asymptotic $\infty$ to asymptotic 0.
See the graph and explanation.

#### Explanation:

To make f real, $x \succ \frac{4}{3}$.

Also,

$y > 0$,

$y \to 0$, as x to oo and#

$y \to \infty$, as$x \to - {\left(\frac{4}{3}\right)}_{+}$.

$y ' = - \frac{3}{4} {\left(3 x + 4\right)}^{- \frac{7}{4}} < 0$.

And so, there are no specific values to be given as as local/global extrema.

graph{1/(3x+4)^0.75 [-10, 10, -5, 5]}