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Calc

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Submitted By gkhatta
Words 491
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Part 1:
1. The average rate of change is the slope between two points and the Leibniz d Notation also called the instantaneous rate of change is the derivative at one single point. Average rate of change always occurs on an interval from one point to another and can be found by calculating the slope of the line passing through the two points. Instantaneous rate of change is the slope of the tangent line at one point that can be found by calculating the derivative of a function at that one single point.
2. Using this example I will approximate the second derivative by duplicating the steps but using the first derivative variables instead.

Part 2:

Rabbit Population

Rabbit Population

1c. The graph plotted is a logistics function because it grows exponentially and then levels off as the x value approaches a saturation point. As the time increases past the saturation point the rabbit population growth rate will continuously decrease causing the rabbit population growth to level off.

2c. The shape of the average rate of change of population curve confirms that the direction of the graph is continuously increasing because all the rates of change are positive. The average rate of change in population growth follows the same rule at the population growth by approaching the limit of 0 as it approaches positive infinity implying the rate of change levels off causing population growth to level off. The average rate of change graph never hits zero so the rabbit population has no stationary points. The point at which the population is growing the fastest is shown at the critical point of the average rate of change curve, the five year time mark.

3c. The significance of this shape confirms that the rate at which the average rate of change is changing at starts decreasing after it intercepts the x coordinate pane. Approximately half way through the fourth year

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