my booklet ask me:

"explain in your own words the process used in this lesson to conclude that the derivative of a cubic function is a quadratic."

the process was just the instantaneous rate of change formula thingy:

f(x + h) - f (x)
h

lim h -> 0 of {(x+h)^3 - x^3}/h
lim h -> 0 of {x^3 + 3hx^2 + 3h^2x + h^3 - x^3}/h
lim h -> 0 of {3hx^2 + 3h^2x + h^3}/h
lim h -> 0 of 3x^2 + 3hx + h^2
3x^2

as far as explaining in your own words, well i guess you can say that -f(x) cancels out the x^3 term of the expanded equation, leaving the next largest power to be x^2

This post was edited by Azrad on Oct 1 2013 06:20pm