Final answer:
To calculate the rate of change of the function f(x) between x = 2 and x = 5, evaluate the function at both points and then find the slope by computing the difference in f(x) values divided by the difference in x values.
Step-by-step explanation:
The question is asking to find the rate of change of the function f(x) = √(2x-3) × 5 between the points where x = 2 and x = 5. To find the rate of change between two points on a function, you calculate the slope of the line that passes through the points that correspond to these values in the function. The slope is found by the difference in the y-values over the difference in the x-values. That is, slope = (f(x2) - f(x1)) / (x2 - x1), where x1 = 2 and x2 = 5.
First, we need to plug in the x-values into the function to find the corresponding y-values.
- f (2) = √ (2(2)-3) × 5 = √1 × 5 = 5
- f (5) = √ (2(5)-3) × 5 = √7 × 5 = 5√7
Next, we use these y-values to find the slope (rate of change).
Slope =
(f (5) - f (2)) / (5 - 2) = (5√7 - 5) / 3
This result represents the rate of change of the function between x = 2 and x = 5.