Mathematics | Senioritis

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...

John Rhodes
June 21, 2023
Calculus

Guide To Determining Concavity With Second Derivative: Step-By-Step Explanation.

Determine Concavity f is concave up: f’ is increasing: f” > 0 (positive)f is concave down: f’ is decreasing: f” < 0 (negative) Concavity is a term...

John Rhodes
June 21, 2023
Calculus

Mastering Curve Sketching: A Guide To Consider Domain, Symmetry, Critical Points, Concavity And More

Determine Function Behavior (Curve Sketching) 1. find critical points (y’=0 or y’ DNE)2. test the regions to see if function incr or decr3. find possible inflection points...

John Rhodes
June 21, 2023
Calculus

Ensuring Well-Defined Compositions: Domain Restrictions In Function Composition – A Math Perspective

When we compose functions, we must make sure that the output of the first function is part of the ___ of the second function. domain When we...