Question

Given the function f(x) = 4x^2 - x + 6, find the expression (f(a + h) - f(a)) / h.

Please provide the expression for (f(a + h) - f(a)) / h in terms of a and h.

Answer 1

To find the expression (f(a + h) - f(a)) / h for the given function f(x) = 4x^2 - x + 6, substitute a + h and a into the function and simplify to get (8a + 4h - 1).

Step-by-step explanation:

To find the expression (f(a + h) - f(a)) / h for the given function f(x) = 4x^2 - x + 6, we need to substitute a + h and a into the function and simplify.

Replacing x with a + h in the function, we get f(a + h) = 4(a + h)^2 - (a + h) + 6.

Replacing x with a in the function, we get f(a) = 4a^2 - a + 6.

Substituting these expressions into the original formula, we have:

(f(a + h) - f(a)) / h = [4(a + h)^2 - (a + h) + 6 - (4a^2 - a + 6)] / h

Simplifying this expression further, we get: (8ah + 4h^2 - h) / h = 8a + 4h - 1.