Question

Simplify the difference quotient f(x)-f(a)/x-a for the given function. f(x)=18x^3

thanks

Answer 1

Do you mean
[ f(x)-f(a)] / [x-a ] ? That would be the slope
[ 18 x^3 - 18 a^3 ] / (x-a)
= 18 [ x^3-a^3 ] / (x-a) = 18 (x^2 + x a + a^2)

Answer 2

note as a ---->x it is 18 (3 x^2) which is the derivative