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Course: Calculus I
Topic: Derivatives
Subtopic: Definition of Derivative

Overview

Calculus I is called Differential Calculus because it's main focus is on differentiating a function resulting in its derivative. This is the process into which we delve today :) In this lesson we introduce derivatives, study the formal definition of derivative, and learn that a derivative is (1) a rate of change, (2) the slope of the tangent line to a curve, and (3) the velocity of a point moving on a curve. Useful stuff in engineering and physical sciences!

Objectives

By the end of this topic you should know and be prepared to be tested on:

Terminology

Terms you should be able to define: secant line, tangent line, point of tangency, slope, derivative, rate of change, differentiation, differentiable, non-differentiable, sharp corner, vertical tangent line, cusp

Text Notes

Mini-Lectures and Examples

STUDY: Definition of Derivative & Tangent Lines & Differentiability

Supplemental Resources (optional)

Video: Definition of Derivative, Selwyn Hollis's Video Calculus

Lesson: Slope of a Tangent Line, Dale Hoffman's Contemporary Calculus
and Definition of Derivative, Dale Hoffman's Contemporary Calculus

rev. 2020-10-10