Final answer:
The percentage rate of change of a function at a given value of x is calculated using the formula: (f'(x)/f(x)) * 100. This measures how much the function's value is changing at that point relative to its current value, converted to a percentage.
Step-by-step explanation:
To calculate the percentage rate of change of a function f(x) at a given value of x, you use the formula:
Percentage rate of change = \((f'(x)/f(x)) \times 100\)
In this formula, f'(x) represents the derivative of the function f(x), which gives the rate of change of the function at a particular x. Then, we divide this rate of change by the function value f(x) at that same point. Multiplying by 100 converts this ratio into a percentage. Let's assume that f(x) is a function representing the amount of money you are paid, and you receive a raise. If the original pay is represented by f(x) and the raise by f'(x), the percentage rate of change would indicate how much of an increase in pay you received, proportionally to your original pay.
If f(x) was $10 per hour, and f'(x) was a $2 increase per hour, plugging these into the formula would yield:
\(\frac{2}{10} \times 100 = 20\%\)
This means that the percentage rate of change in your pay rate is 20%.
So the correct answer is:
a) Percentage rate = (f'(x)/f(x)) * 100