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

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Answer 1 · 2017-01-05T14:34:30

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