Mastering Extrema and Optimization in Calculus

Optimization refers to using derivatives as a tool to find the highest or lowest points on a graph.

Relative extrema are points on a graph where a function has a local maximum or minimum.

A point on a graph is a relative maximum if the function is decreasing on one side of the point and increasing on the other side. It is a relative minimum if the function is increasing on one side and decreasing on the other side.

<p>No, we cannot determine if a point on a graph is an extremum just by looking at the x-coordinate. We need to consider the behavior of the function near that point to make that determination.</p> Signup and view all the answers

<p>To find the extrema of a function without the graph, we need to use calculus techniques such as finding the derivative, setting it equal to zero, and solving for the critical points.</p> Signup and view all the answers