John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 31, 2023
Calculus

Understanding the Relationship between Decreasing Derivative and Negative or Decreasing Second Derivative in Math

If f'(x) is decreasing, then f”(x) is? If the derivative, f'(x), is decreasing, it means that its slope is decreasing as x increases If the derivative, f'(x),...

John Rhodes
July 31, 2023
Calculus

Exploring the Concept of Continuity in Mathematics | Smooth Transitions and Predictable Behavior of Functions

Continuity Definition In mathematics, continuity refers to how a function behaves without any disruptions or breaks In mathematics, continuity refers to how a function behaves without any...

John Rhodes
July 31, 2023
Calculus

The Intermediate Value Theorem | Application and Examples in Calculus and Real Analysis

Intermediate Value Theorem The Intermediate Value Theorem (IVT) is a fundamental concept in calculus and real analysis The Intermediate Value Theorem (IVT) is a fundamental concept in...

John Rhodes
July 31, 2023
Calculus

Understanding Velocity | Definition, Formula, and Importance

What is velocity? Velocity is a physical quantity that describes the rate at which an object changes its position in a specific direction Velocity is a physical...

John Rhodes
July 31, 2023
Calculus

Understanding the Limit Definition of Derivative | A Comprehensive Guide to Calculating Derivatives and Analyzing Function Behavior

Limit Definition of Derivative The limit definition of derivative is a mathematical expression that defines the derivative of a function at a particular point The limit definition...

John Rhodes
July 31, 2023
Calculus

How the Intermediate Value Theorem Enhances Understanding of Continuous Functions and Their Solutions

The IVT implies… The Intermediate Value Theorem (IVT) is a fundamental theorem in calculus that applies to continuous functions The Intermediate Value Theorem (IVT) is a fundamental...

John Rhodes
July 31, 2023
Calculus

Understanding Differentiability in Mathematics | Common Scenarios Where Functions Fail to be Differentiable

When is a function not differentiable? A function is not differentiable at a particular point if it fails to meet one or more conditions necessary for differentiation...

John Rhodes
July 31, 2023
Calculus

Understanding the Basics | Four Derivative Rules in Calculus for Calculating Rates of Change

What are the four basic derivative rules? The four basic derivative rules in calculus are: 1 The four basic derivative rules in calculus are: 1. Power Rule:...