Question

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

Answer 1

There are no specific values as local/global extrema.
Continuously f `darr`, from asymptotic `oo` to asymptotic 0.
See the graph and explanation.

Explanation:

To make f real, `x >-4/3`.

Also,

`y > 0`,

`y to 0`, as x to oo and#

`y to oo`, as`x to-(4/3)_+`.

`y'=-3/4(3x+4)^(-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]}