Question

How do you find the local max and min for `f(x)= 5x - 3`?

Answer 1

There are none

Explanation:

y = 5x - 3 , is the equation of a straight line , in the form y = mx + c , and as such has no stationary points.
Here is it's graph.
graph{5x-3 [-10, 10, -5, 5]}