Calculus | Senioritis

John Rhodes
July 30, 2023
Calculus

Understanding the Formal Definition of Derivative | Calculating Rate of Change and Tangent Line Slope

formal version of def. of derivative The formal definition of the derivative of a function f(x) at a point x = c is given by the limit:...

John Rhodes
July 30, 2023
Calculus

Understanding the Derivative | Exploring the Fundamental Concept of Calculus

alternate version of def. of derivative The derivative of a function is a fundamental concept in calculus that measures the rate of change of the function at...

John Rhodes
July 30, 2023
Calculus

Understanding Continuity | A Fundamental Concept in Calculus and Real Analysis

definition of continuity: f is continuous at c iff the limit of f(x) as x approaches c exists and is equal to f(c) the limit of f(x)...

John Rhodes
July 30, 2023
Calculus

Using the Product Rule to Find the Derivative of the Product of Two Functions

d/dx [uv] To find the derivative of the product of two functions, u(x) and v(x), we use the product rule To find the derivative of the product...

John Rhodes
July 30, 2023
Calculus

How to Find the Derivative of the Composition of Two Functions using the Chain Rule

d/dx f(g(x)) The expression “d/dx f(g(x))” represents the derivative of the composition of two functions, f(x) and g(x), with respect to the independent variable x The expression...

John Rhodes
July 30, 2023
Calculus

The Relationship Between Increasing Functions and Positive Derivatives | A Comprehensive Explanation

If f(x) is increasing, then f'(x) is If a function f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase If...

John Rhodes
July 30, 2023
Calculus

Understanding the Relationship between a Negative Function and its Derivative | Exploring Decreasing Trends and Negative Outputs

f'(x) is negative if f(x) is If the function f(x) is negative, it means that the y-values or outputs of the function are negative for certain values...

John Rhodes
July 30, 2023
Calculus

Understanding the Relationship between f(x) and the Positivity of f(x)

f”(x) is positive if f(x) is To understand whether f”(x) is positive when f(x) is positive, let’s start by understanding what the notation f”(x) represents To understand...