Question

Given that () = 3² - 4, evaluate the difference quotient ()−()/- for ≠ a. Also, convert −60 degrees to radians and express your answer as a fraction in lowest terms.

Answer 1

The difference quotient for f(x) = 3² - 4 with x ≠ a, is zero since f(x) and f(a) yield the same result. Converting -60 degrees to radians gives -π/3.

Step-by-step explanation:

Evaluating the Difference Quotient

To evaluate the difference quotient f(x) - f(a) / (x - a) for f(x) = 3² - 4 and x ≠ a, we need to follow these steps:

1. Substitute x into the function: f(x) = 3² - 4 = 9 - 4 = 5.
2. Substitute a into the function: f(a) = 3² - 4 = 9 - 4 = 5 (Note: As no specific value for a is given and there is no x variable actually in f(x), f(x) and f(a) will yield the same result).
3. Insert the results into the difference quotient formula: (f(x) - f(a)) / (x - a) = (5 - 5) / (x - a) = 0 / (x - a) = 0 as the numerator is zero.

Converting Degrees to Radians

To convert -60 degrees to radians, we use the conversion factor π radians = 180 degrees. Therefore:

-60 degrees × (π/180 degrees) = -π/3 radians.

This is the expression in radians in lowest terms.