Question

Question #fd5fd

Answer 1

Local extrema is when the instantaneous slope of the function at that point is 0. Absolute extrema is the biggest or smallest point in the entire graph or interval.

Explanation:

graph{(x-1)^3 - x^2 + x -1 [-10, 10, -5, 5]}

For example, in this graph, `f(x) = (x-1)^3 - x^2 + x - 1`, let's think about the interval [-1, 3].

You can see two points where the graph is flat and the instantaneous slope is at 0. One is the local maxima, `(0.667, -0.815)`, and the other one is the local minima, `(2, -2)`.

However, these are not the lowest or highest points in the entire interval. The absolute maxima is `(3, 1)`, while the absolute minima is `(-1, -11)`.

Hope this helped.