Question

For the following exercises, use a graphing utility to estimate the local extrema of each function and to estimate the intervals on which the function is increasing and decreasing k(t)= 3t^2/3 - t​

Answer 1

Point (0,0) is a local minimum and point (8,4) is a local maximum.

The function is incrasing for all
`0<x<8`

The function is decreasing for all
`x<0\text{ or }x>8`

Explanation:

Plot the graph of the function
`k(t)=3\cdot t^{(2)/(3)}-t` (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
`0<x<8`

The function is decreasing for all
`x<0\text{ or }x>8`