Final answer:
The average rate of change of the function f(x)=-2x^2+3/x on the interval [3,4] is -34.75.
Step-by-step explanation:
To calculate the average rate of change of the function f(x)=-2x^2+3/x on the interval [3,4], we can use the formula:
Average Rate of Change = (f(4) - f(3))/(4 - 3)
Substituting the values in, we get:
Average Rate of Change = (-2(4)^2+3/(4)) - (-2(3)^2+3/(3))/(4 - 3)
Simplifying, we get:
Average Rate of Change = (-32 + 3/4) - (-18 + 3/3)
Therefore, the average rate of change of the function on the interval [3,4] is -34.75.