Calculus question, PLEASE help?

Question

Given the function f(x) = x^3 with a and x in the domain, a doesn’t equal x, then what does f(x) – f(a)/x – a equal?

Answer 1

it equals the slope of the line joining the two points (x,f(x)) and (a,f(a))

Answer 2

f(x) = x^3

Calculating [f(x) - f(a)] / (x - a), we get

[ x^3 - a^3 ] / (x - a)

Factor the top as a difference of cubes,

[(x - a)(x^2 + ax + a^2)] / (x - a)

Since x does not equal a, we can cancel the common factor of x - a on the top and bottom.

x^2 + ax + a^2

That is precisely what [f(x) - f(a)]/(x - a) equals.