16 mark for review of the following points, at which is the rate of change of g the least? a a b b c c d d…

16 mark for review of the following points, at which is the rate of change of g the least? a a b b c c d d the figure shows the graph of a function g in the xy - plane with four labeled points. it is known that a relative maximum of g occurs at a, and the only point of inflection of the graph of g is c.

16 mark for review of the following points, at which is the rate of change of g the least? a a b b c c d d the figure shows the graph of a function g in the xy - plane with four labeled points. it is known that a relative maximum of g occurs at a, and the only point of inflection of the graph of g is c.

Answer

Explanation:

Step1: Recall rate - of - change concept

The rate of change of a function at a point is given by the slope of the tangent line to the graph of the function at that point.

Step2: Analyze slope at each point

At point A, the function has a relative maximum, so the slope of the tangent line is 0. At point B, the function is decreasing, so the slope of the tangent line is negative. At point C, it is an inflection point, and the slope of the tangent line is negative. At point D, the function is increasing, so the slope of the tangent line is positive.

Step3: Compare slopes

Since 0 is greater than any negative number and we are looking for the least rate of change (the most negative or the smallest non - negative value), the rate of change is least at the point where the slope is the most negative or the smallest non - negative. Among the points, the slope at point A is 0, and the slopes at B and C are negative, and the slope at D is positive. So the rate of change is least at A.

Answer:

A. A