Question

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

A) (0.5, 7), minimum; (2, 1), point of inflection; (3.5, -5), maximum.

B) (0.5, 7), maximum; (2, 1), point of inflection; (3.5, -5), minimum.

C) (0.5, 7), maximum; (3.5, -5) minimum.

D) no critical points.

*Please show any and all work, thank you.*​

Answer 1

Answer: B

(0.5, 7), maximum; (2, 1), point of inflection; (3.5, –5), minimum

Critical points of a function are those points at which a line drawn tangent to the curve is horizontal or vertical. On the graph, maximum and minimum points look like peaks and valleys, respectively. Points of inflection that are critical points are places where the curve flattens out and changes from being bent upward to being bent downward or vice versa.

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