Mathematics | Senioritis

John Rhodes
June 21, 2023
Calculus

The Gradient Vector And Its Applications In Mathematics And Engineering

Gradient vector Gives the direction of the directional derivative The gradient vector is a vector that points in the direction of maximum increase of a scalar field....

John Rhodes
June 21, 2023
Calculus

Learn How To Calculate The Gradient Vector Of A Scalar Function – Step By Step Guide

Calculating gradient vector The gradient vector is a vector that points in the direction of the greatest rate of increase of a scalar function. It is a...

John Rhodes
June 21, 2023
Calculus

How To Find The Vector With Maximum Steepness Using Directional Derivatives And Gradient Vectors In Math Functions

Find vector with maximum steepness The gradient vector at that point To find the vector with maximum steepness, we need to first define what we mean by...

John Rhodes
June 21, 2023
Calculus

Finding Maximum Rate Of Change: Derivatives And Analysis Of Mathematical Functions

Find max rate of change Magnitude of gradient vector To find the maximum rate of change, we need to take the derivative of the function and then...

John Rhodes
June 21, 2023
Calculus

How To Perform The Second Derivative Test To Find Critical Points Of A Function: Steps And Guidelines

Second Derivative Test D(x,y) = fxx(x,y) * fyy(x,y) – (fxy(x,y))^2 – D(x,y) > 0, fxx(x,y) > 0 => local maximum – D(x,y) > 0, fxx(x,y) < 0...

John Rhodes
June 21, 2023
Calculus

The Fundamental Theorem For Extreme Values: Maximum And Minimum Values Of Continuous Functions On Closed Intervals

Extreme Value Theorem If f is continuous on [a,b] then f has an absolute maximum and an absolute minimum on [a,b]. The global extrema occur at critical...

John Rhodes
June 21, 2023
Calculus

Maximizing Math: A Comprehensive Guide To Finding Extrema Of Univariate Functions

Find extrema Set fx(x,y) and fy(x,y) to 0, plug in boundaries of x and y into original function. To find the extrema of a function, you need...

John Rhodes
June 21, 2023
Calculus

Maximize And Minimize Functions: A Step-By-Step Guide With An Example

Find max/min value Plug point original function To find the maximum or minimum value of a function, we need to take the derivative of the function and...