textbook-theory · English
The Notion of a Derivative and Cubic Functions
A two-page lecture handout covering the general definition of the derivative as the limit of a difference quotient, with graphical illustration of secant-line approximations to the tangent. It then introduces cubic functions f(x) = ax³ + bx² + cx + d, describes the three basic graph forms, and derives the formula df/dx(p) = 3ap² + 2bp + c, working through examples with g(x) = x³ + 3x and h(x) = x³ − 3x.
calculusderivativescubic functionstangent lines