Question

Find the average rate of change for the function over the given interval.y=4x² between x=0 and x= 7/4?

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Answer 1

The average rate of change of the function y=4x² from x=0 to x=7/4 is calculated by finding the change in y and the change in x, then dividing the two. The result is 7.

Step-by-step explanation:

To find the average rate of change of the function y=4x² over the interval from x=0 to x=7/4, we use the formula for the average rate of change, which is:

average rate of change = (change in y) / (change in x)

First, we calculate the value of the function at the start and end of the interval:

• y(0) = 4(0)² = 0
• y(7/4) = 4(7/4)² = 4(49/16) = 49/4

Then, we find the change in y and the change in x:

• Change in y: y(7/4) - y(0) = 49/4 - 0 = 49/4
• Change in x: (7/4) - 0 = 7/4

Now, we can calculate the average rate of change:

average rate of change = (49/4) / (7/4) = 49/7 = 7

Therefore, the average rate of change of the function y = 4x² from x = 0 to x = 7/4 is 7.