Question

F(x)=8x^(2)-x+4 (a) Find the difference quotient (f(x)-f(a))/(x-a) for the function,

Answer 1

The difference quotient (f(x) - f(a)) / (x - a) for the function f(x) = 8x^2 - x + 4 is calculated by substituting f(x) and f(a) into the formula and simplifying.

Step-by-step explanation:

The difference quotient for the function f(x) = 8x^2 - x + 4 is defined as (f(x) - f(a)) / (x - a). To find this, we substitute the function into the formula:

1. Calculate f(x): f(x) = 8x^2 - x + 4.
2. Calculate f(a): f(a) = 8a^2 - a + 4.
3. Subtract f(a) from f(x): f(x) - f(a) = (8x^2 - x + 4) - (8a^2 - a + 4).
4. Simplify the expression: f(x) - f(a) = 8x^2 - x - 8a^2 + a.
5. Divide the result by x-a: (f(x) - f(a)) / (x - a) = (8x^2 - 8a^2 - x + a) / (x - a).

This gives the difference quotient for the function, which simplifies further depending on the values of x and a.