Estimate and classify the critical points for the graph of the function.

can someone explain how to find the answer.
you.

  (-1, 2) — derivative is zero

Step-by-step explanation:

A critical point of a function is a point at which the slope is zero or undefined. (The critical point must actually be in the domain of the function. Vertical asymptotes are not critical points.)

You find the answer by looking for points on the graph where a tangent to the function is horizontal or vertical.

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In the given graph, the curve approaches horizontal near the point (-1, 2), so it is reasonable to estimate that that point is a critical point.

The attached graph also shows the inverse function. That has a critical point at (2, -1), where the slope is undefined (a tangent to the graph is vertical).

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The graph of a circle or ellipse does not pass the vertical line test, so is not a function. However, the graph still has critical points where the tangents are vertical or horizontal. The second attachment shows those critical points.