   Chapter 2.1, Problem 17E

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# For the function g whose graph is given, arrange the following numbers in increasing order and explain your reasoning: To determine

To arrange:

0, g'(-2), g'(0), g'(2), g'(4)  in increasing order.

Explanation

1) Concept:

We know that g 'x=limh0gx+h-g(x)h. Recall that the derivative is instantaneous rate of change of a function. Also recall that the derivative at a point is the slope of tangent at the given point.

2) Calculation:

At x = 0, the function is decreasing so the rate of change of function is negative so g'0=limh0gh-g(0)h<0

At x = -2, The function is increasing. So the rate of change is positive. Also the graph of g at -2 is steeper compared to the x = 2 and x = 4. So the rate of change of g at -2 that is slope at -2 is more than the rate of change at 2 and 4

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