John Rhodes, Math Teacher at Senioritis.io

John Rhodes
June 21, 2023
Linear Algebra

Master The Associative Property Of Multiplication In Algebra

(AB)C = (AC)B The statement “(AB)C = (AC)B” is not universally true. The statement “(AB)C = (AC)B” is not universally true. In general, the order of matrix...

John Rhodes
June 21, 2023
Linear Algebra

Proving (Ab)^T = A^T * B^T For Matrices A And B

(AB)^T = A^T * B^T The statement “(AB)^T = A^T * B^T” is true. The statement “(AB)^T = A^T * B^T” is true. The transpose of a...

John Rhodes
June 21, 2023
Linear Algebra

The Transpose Of Matrix Sum: Proof That (A+B)T = At + Bt

The transpose of a sum of matrices equals the sum of their transposes. True according to Theorem 3B which says that the transpose of a sum of...

John Rhodes
June 21, 2023
Calculus

How To Use The Quotient Rule For Finding Derivatives In Calculus

Quotient rule of f(x)/g(x) g(x)f'(x)-f(x)g'(x)/g(x)² The quotient rule is a formula used in differential calculus to find the derivative of a function that is in the form...

John Rhodes
June 21, 2023
Calculus

Discover The Power Of The Intermediate Value Theorem In Calculus

Intermediate Value Theorem if f(x) is continuous on [a,b], then there will be a point x=c that lies in between [a,b] such that f(c) is between f(a)...

John Rhodes
June 21, 2023
Calculus

Maximizing And Minimizing Functions: The Significance Of The Extreme Value Theorem In Calculus Optimization

Extreme Value Theorem if f(x) is continuous on [a,b], then f(x) has an absolute max or min on the interval The Extreme Value Theorem is a fundamental...

John Rhodes
June 21, 2023
Calculus

How Rolle’S Theorem Helps Find Horizontal Tangents And Multiple Roots Of Polynomial Equations In Calculus

Rolle’s Theorem if f(x) is continuous on [a,b] and differentiable on (a,b), and if f(a)=f(b), then there is at least one point (x=c) on (a,b) where f'(c)=0...

John Rhodes
June 21, 2023
Calculus

The Power Of Mean Value Theorem In Calculus Optimization: Finding Critical Points And Extrema

Mean Value Theorem if f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one point (x=c) where f'(c)= f(b)-f(a)/b-a The Mean Value Theorem...