Answer:
The average rate of change of the function y = 2x^2 + 1 over the interval from x = -4 to x = 0 is 8.
Explanation:
The average rate of change of the function y = 2x^2 + 1 over the interval from x = -4 to x = 0 can be calculated using the formula:
Average Rate of Change = (f(b) - f(a)) / (b - a)
where f(x) represents the function and a and b represent the interval endpoints.
In this case, the interval is from x = -4 to x = 0. Substituting these values into the formula:
Average Rate of Change = (f(0) - f(-4)) / (0 - (-4))
To calculate the average rate of change, we need to find the values of f(0) and f(-4) by substituting these values into the function:
f(0) = 2(0)^2 + 1 = 1 f(-4) = 2(-4)^2 + 1 = 33
Substituting these values into the formula:
Average Rate of Change = (33 - 1) / (0 - (-4)) = 32 / 4 = 8
Therefore, the average rate of change of the function y = 2x^2 + 1 over the interval from x = -4 to x = 0 is 8.
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