Final answer:
The average rate of change of the function g(x) = 8x^4 + 3 on the interval [-2,4] is calculated to be 320. However, this answer does not match the provided choices, indicating a possible error either in the options given or in the calculation.
Step-by-step explanation:
To find the average rate of change of the function g(x) = 8x⁴ + 3 on the interval [-2,4], we apply the formula for the average rate of change:
Average rate of change = \( \frac{g(b) - g(a)}{b - a} \)
Here, \(a = -2\) and \(b = 4\), so we need to calculate \(g(4)\) and \(g(-2)\):
\(g(4) = 8(4)^4 + 3 = 8(256) + 3 = 2048 + 3 = 2051\)
\(g(-2) = 8(-2)^4 + 3 = 8(16) + 3 = 128 + 3 = 131\)
Now we will use these values to find the average rate of change:
Average rate of change = \( \frac{2051 - 131}{4 - (-2)} = \frac{1920}{6} = 320\)
However, the given options do not include 320. There might be a calculation mistake, so let's recheck it:
\(g(b) - g(a) = 2051 - 131 = 1920\)
\(b - a = 4 - (-2) = 4 + 2 = 6\)
Average rate of change = \( \frac{1920}{6} = 320 \)
The correct answer is 320, although option a. 324 is closest to our calculated answer, there seems to be a discrepancy as 320 is not listed as a choice. It might be necessary to review the choices provided or recheck the calculation method.