Final answer:
The difference quotient for the function f(x) = -8x + 1 is -8. This is computed by finding f(x + h) - f(x) and dividing by h, which simplifies to -8, indicating that the derivative of the function is -8.
Step-by-step explanation:
The question asks to find the difference quotient for the function f(x) = -8x + 1, which is a common task in calculus to explore the derivative of the function. To find the difference quotient, we compute f(x + h) - f(x) and divide the result by h, where h is not equal to 0. The functions provided in various parts of the question seem irrelevant, however, we will stay focused on the given function f(x).
Calculating f(x + h):
- f(x + h) = -8(x + h) + 1 = -8x - 8h + 1
Then, the difference quotient is calculated:
- ((-8x - 8h + 1) - (-8x + 1)) / h
- The -8x and +8x will cancel each other out, simplifying to (-8h) / h
- This further simplifies to -8, since the h's cancel out.
Therefore, the difference quotient for the function f(x) = -8x + 1 is -8, which is also the derivative of the function.