Answer:
the average rate of change of f(x) on [a, a+h] is 4a + 2h + 5.
Explanation:
The average rate of change of a function f(x) on the interval [a, a+h] is given by the formula:
[f(a+h) - f(a)] / h
So, for the function f(x) = 2x^2 + 5x - 3, we have:
[f(a+h) - f(a)] / h
= [2(a+h)^2 + 5(a+h) - 3 - (2a^2 + 5a - 3)] / h
= [2a^2 + 4ah + 2h^2 + 5a + 5h - 3 - 2a^2 - 5a + 3] / h
= [4ah + 2h^2 + 5h] / h
= 4a + 2h + 5
Therefore, the average rate of change of f(x) on [a, a+h] is 4a + 2h + 5.