Answer:
Point (0,0) is a local minimum and point (8,4) is a local maximum.
The function is incrasing for all [tex]0<x<8[/tex]
The function is decreasing for all [tex]x<0\text{ or }x>8[/tex]
Step-by-step explanation:
Plot the graph of the function [tex]k(t)=3\cdot t^{\frac{2}{3}}-t[/tex] (see attached diagram for details).
A local extremum is a local maximum or a local minimum.
From the graph of the function, you can see that point (0,0) is a local minimum and point (8,4) is a local maximum.
The function is incrasing for all [tex]0<x<8[/tex]
The function is decreasing for all [tex]x<0\text{ or }x>8[/tex]
