John Rhodes, Math Teacher at Senioritis.io

John Rhodes
July 30, 2023
Calculus

The Relationship Between Increasing Functions and Positive Derivatives | A Comprehensive Explanation

If f(x) is increasing, then f'(x) is If a function f(x) is increasing, it means that as x increases, the corresponding values of f(x) also increase If...

John Rhodes
July 30, 2023
Calculus

Understanding Concavity | Exploring Curvature Transitions in Mathematical Functions

If f(x) has an inflection point, then f(x) has change in concavity concavity. Change in concavity refers to a transition in the direction of the curvature of...

John Rhodes
July 30, 2023
Calculus

Understanding the Relationship between f(x) and the Positivity of f(x)

f”(x) is positive if f(x) is To understand whether f”(x) is positive when f(x) is positive, let’s start by understanding what the notation f”(x) represents To understand...

John Rhodes
July 30, 2023
Calculus

Understanding the Significance of f'(a) = 0 | Exploring the Behavior of a Function at x=a

If f'(a) = 0, then f(x) has a If f'(a) = 0, this means that the derivative of the function f(x) at the point x=a is 0...

John Rhodes
July 30, 2023
Calculus

Why f'(a) does not exist at a corner or a cusp in a function f(x)

if f(x) has a corner or cusp at x = a, then f'(a) is If a function f(x) has a corner or cusp at x = a,...

John Rhodes
July 30, 2023
Calculus

Understanding the Relationship Between f'(x) and Local Extrema in Functions

If f'(x) has a change of sign and is always defined, then f(x) has either a If f'(x) has a change of sign and is always defined,...

John Rhodes
July 30, 2023
Calculus

Differentiation of g(x) and Finding g'(a) – Math Tutorial for Calculating Derivatives and Substituting Values

If f'(a)=2 and g(x)=f(x)-5, then g'(a) = To find the value of g'(a), we need to differentiate the function g(x) with respect to x and then substitute...

John Rhodes
July 30, 2023
Calculus

Understanding Critical Points in Mathematics | Definition and Analysis Techniques

If f'(x) = 0 for all values of x, then f(x) is If the derivative of a function f(x) is equal to 0 for all values of...