John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Calculus

The Mean Value Theorem (Mvt): The Relationship Between Average And Slope In Calculus

(MVT) Mean Value Theorem f is continuous on [a,b]differentiable on (a,b)x=a and x=b joined by secant linethere must exist at least one point c between them such...

John Rhodes
June 21, 2023
Calculus

The Extreme Value Theorem: Guaranteeing Maximum And Minimum Values For Calculus And Real Analysis With Practical Applications In Economics, Physics, And Engineering

Extreme Value Theorem f is continuous on [a,b]f has an absolute minimum and an absolute maximum on [a,b] The Extreme Value Theorem is a fundamental theorem in...

John Rhodes
June 21, 2023
Calculus

Discovering Critical Points With Rolle’S Theorem: A Useful Tool In Calculus

Rolle’s Theorem f is continuous on [a,b]differentiable on (a.b)f(a)=f(b)there is a number c between them such that f'(c)=0*specific case of MVT where endpoints are equal Rolle’s Theorem...

John Rhodes
June 21, 2023
Calculus

Mastering The First Derivative Test: Analyzing Function Behavior At Critical Points

First Derivative Test (function behavior) f'(c)=0 –> x=c is a critical point of f(x)f'(x)>0 for all x in interval (a.b) –> f(x) is increasing on [a,b]f'(x) f(x)...

John Rhodes
June 21, 2023
Calculus

Finding Absolute Extrema Of Functions: Step-By-Step Guide With Example

Candidates Test (absolute extrema) 1. verify f is continuous on [a.b]2. find all critical points on [a,b]3. evaluate f at the critical points AND endpoints4. identify absolute...

John Rhodes
June 21, 2023
Calculus

Mastering The Second Derivative Test: Analyzing Function Behavior And Critical Points

Second Derivative Test (concavity, local extrema) f'(c)=0 and f”(c) local max at x=cf'(c)=0 and f”(c)>0 (conc up) –> local min at x=c*if f”(c)=0 SDT cannot be used...

John Rhodes
June 21, 2023
Calculus

Master Optimization Problems For Math: Techniques, Constraints, And Decision Variables Explained

Optimization Problems 1. draw a picture as needed2. label any values and variables (as few variables as possible)3. find formula, identify domain4. rewrite formula in terms of...

John Rhodes
June 21, 2023
Calculus

Implicit Relations In Mathematics: Definition, Examples, And Applications

Implicit Relations if f’=0 or f’ DNE –> critical pointif f”>0 concave up An implicit relation is a mathematical equation in which the dependent variable is not...