Mathematics | Senioritis

John Rhodes
June 21, 2023
Trigonometry

Simplify Trigonometric Expressions With The Double Angle Identity For Cosine

Double Angle Identity for Cosine III (cos) cos2x=2cos^2(x)-1 The double angle identity for cosine provides a way to express the cosine of a angle in terms of...

John Rhodes
June 21, 2023
Calculus

Master The Intermediate Value Theorem: Proving Existence Of Solutions And Analyzing Functions

Intermediate Value Theorem If f(1)4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis. The Intermediate Value Theorem (IVT)...

John Rhodes
June 21, 2023
Calculus

Average Rate Of Change In Mathematics: Formula And Concepts Explained

Average Rate of Change Slope of secant line between two points, use to estimate instantanous rate of change at a point. The average rate of change is...

John Rhodes
June 21, 2023
Calculus

The Instantaneous Rate Of Change: A Key Concept In Mathematics And Its Applications In Various Fields

Instantenous Rate of Change Slope of tangent line at a point, value of derivative at a point The instantaneous rate of change is a mathematical concept that...

John Rhodes
June 21, 2023
Calculus

The Formal Definition Of Derivatives In Mathematics: Calculating Instantaneous Rates Of Change

Formal definition of derivative limit as h approaches 0 of [f(a+h)-f(a)]/h The formal definition of a derivative is the limit of the ratio of the change in...

John Rhodes
June 21, 2023
Calculus

Increasing Functions In Calculus: Positive Derivatives And Upward Slopes

When f ‘(x) is positive, f(x) is increasing When f ‘(x) is positive, it means that the function f(x) is increasing at that point x. In other...

John Rhodes
June 21, 2023
Calculus

The Significance Of F'(X) Being Negative In Math: Implications For Function Decrease

When f ‘(x) is negative, f(x) is decreasing When f'(x) is negative, it means that the slope of the graph of the function f(x) is negative at...

John Rhodes
June 21, 2023
Calculus

Local Minimum: How The Function’S Slope Determines Its Lowest Point

When f ‘(x) changes from negative to positive, f(x) has a relative minimum When the derivative of a function, f ‘(x), changes from negative to positive at...