Final answer:
To find the rate of change for the function f(x) = 5√(2x-3) between x = 2 and 5, substitute these values into the function to calculate the average rate of change. The correct formula is (f(5) - f(2)) / (5 - 2).
Step-by-step explanation:
The question asks to find the rate of change of the function f(x) = √(2x-3) × 5 between x = 2 and x = 5. To find this, you would calculate the average rate of change using the function's values at these points. This involves substituting x = 2 and x = 5 into the function to get f(2) and f(5), respectively, and then using the formula:
average rate of change = ∆f / ∆x = (f(5) - f(2)) / (5 - 2)
However, there seems to be a difficulty with the function as provided. The expression √(2x-3) × 5 does not appear to be properly formatted as it combines a square root and multiplication in a manner that is unclear. Assuming the function should be f(x) = 5√(2x-3), we can proceed:
f(2) = 5√(2×2 - 3) = 5√1 = 5
f(5) = 5√(2×5 - 3) = 5√7
Now, calculate the average rate of change:
average rate of change = (5√7 - 5) / (5 - 2) = (5(√7 - 1)) / 3
This gives the average rate of change of the function between x = 2 and x = 5.