MAT101 – Mathematics-I

Derivative

Two basic problems

Rate of Change

Rate of Change: Revenue Analysis

Rate of Change: Revenue Analysis

Rate of Change

Tangent and Secant Line

Slope of the Secant Line

Slope of the Secant Line: Example

Slope of the Secant Line: Example

Slope of the Secant Line: Example

(D) In part (C), we saw that the limit of the slopes of the secant lines through the point (1, f(1)) is 2. If we graph the line through (1, f(1)) with slope 2, then this line is the limit of the secant lines. The slope obtained from the limit of slopes of secant lines is called the slope of the graph at x = 1. The line through the point (1, f(1)) with this slope is called the tangent line.

Slope of the Tangent Line and Derivative

Derivative: Summary

Derivative: Example

Derivative: Example

Derivative: Example

Derivative Example: Sales Analysis

Nonexistence of the Derivative

Nonexistence of the Derivative

Nonexistence of the Derivative

Basic Differentiation Properties

Basic Differentiation Properties

Basic Differentiation Properties: Examples

Basic Differentiation Properties: Examples

Basic Differentiation Properties: Examples

Basic Differentiation Properties: Examples

Marginal Analysis in Business and Economics

Marginal Analysis in Business and Economics

Marginal Analysis in Business and Economics

Marginal Analysis in Business and Economics

Marginal Analysis in Business and Economics

Marginal Analysis in Business and Economics: Example

Marginal Analysis in Business and Economics: Example

Marginal Average Cost, Revenue, and Profit

Marginal Average Cost, Revenue, and Profit: Example

Marginal Average Cost, Revenue, and Profit: Example