I need help!! Describe how to determine the average rate of change between x = 1 and x = 3 for the function f(x) = 3x^3 + 1. Include the average rate of change in your answer.

The average rate of change obtained from the ratio of the change in y to the change in x is 39.

The average rate of change can be obtained using the relation :

Rate of change = (y2 - y1) ÷ (x2 - x1)

At ; x1 = 1

y1 can be calculated from the function ;

y1 = 3(1³) + 1 = 3(1) + 1 = 4

At ; x2 = 3

y1 can be calculated from the function ;

y2 = 3(3³) + 1 = 3(27) + 1 = 82

Rate of change can be calculated thus :

Slope = (82 - 4) ÷ (3 - 1) = 78 ÷ 2 = 39

Therefore, the average rate of change is 39.

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39

Step-by-step explanation:

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: