Mathematics | Senioritis

John Rhodes
June 21, 2023
Calculus

Mastering Arithmetic Mean: The Basics And Importance Of Calculating Averages In Statistical Analysis

Arithmetic Mean The arithmetic mean of two numbers a and b is (a+b)/2. Arithmetic mean is a measure of central tendency which represents the average of a...

John Rhodes
June 21, 2023
Calculus

Optimizing Your Math Knowledge: The Concavity Test For Graph Curvature.

Concavity Test The graph of a twice-differentiable function y = f(x) is:(a) concave up on any interval where y > 0(b) concave down on any interval where...

John Rhodes
June 21, 2023
Calculus

Decreasing Functions: Definition And Examples In Mathematics

Decreasing Function Let f be a function defined on an interval I and let x₁ and x₂ be any two points in I. F decreases on I...

John Rhodes
June 21, 2023
Calculus

Master The Basics Of Differential Calculus: Derivatives And Their Applications

Differential If y = f(x) is a differentiable function, the differential dx is an independent variable and the differential dy is dy = f'(x) dx. Differential generally...

John Rhodes
June 21, 2023
Calculus

Mastering The Extreme Value Theorem: Guaranteeing Maximum And Minimum Values Of Continuous Functions

Extreme Value Theorem If f is continuous on a closed interval [a,b], then f has both a maximum value and a minimum value on the interval. The...

John Rhodes
June 21, 2023
Calculus

Mastering The First Derivative Test: Analyzing Critical Points Of Functions

First Derivative Test For a continuous function f.(1)if f’ changes sign from positive to negative at a critical point c, then f has a local maximum value...

John Rhodes
June 21, 2023
Calculus

Mastering Linearization: Techniques For Simplifying Complex Nonlinear Systems

Linearization The approximating function L(x) = f(a) + f'(a)(x – a) when f is differentiable at x = a. Linearization is a mathematical technique used to approximate...

John Rhodes
June 21, 2023
Calculus

Learn How To Find The Derivative Of Ln(U) Using The Chain Rule Of Differentiation

derv (ln u) (u’)/u To find the derivative of ln(u), where u is a function of some variable x. Using the chain rule of differentiation, we have:...