Mathematics | Senioritis

John Rhodes
June 21, 2023
Calculus

Calculus: Why Increasing Functions Have Positive Derivatives

If f(x) is increasing, then f'(x) is? f”(x) = positive If f(x) is increasing, that means the values of f(x) are getting larger as x is increasing....

John Rhodes
June 21, 2023
Calculus

The Relationship Between Decreasing Functions And Negative Derivatives In Calculus

If f(x) is decreasing, then f'(x) is? f”(x) = negative If f(x) is a differentiable function and it is decreasing, then its derivative, f'(x), must be negative....

John Rhodes
June 21, 2023
Calculus

Concave Up Functions: The Relationship Between Second Derivative And Graph Shape

If f(x) is concave up, then f”(x) is? f”(x) = positive If a function f(x) is concave up, then it means that its graph is shaped like...

John Rhodes
June 21, 2023
Calculus

Concave Down Functions: The Role Of Second Derivative F”(X)

If f(x) is concave down, then f”(x) is? f”(x) = negative If a function f(x) is concave down, it means that it is curving downwards or has...

John Rhodes
June 21, 2023
Calculus

Why F'(X) Being Increasing Implies That F”(X) Is Positive? | Explanation And Example

If f'(x) is increasing, then f”(x) is? y-f(a)=f'(a)(x-a) If f'(x) is increasing, then f”(x) is positive. To explain this, let’s first define what it means for a...

John Rhodes
June 21, 2023
Calculus

How Decreasing F'(X) Indicates Negative F”(X) For Graphs Of Functions – An Explanation For Math Enthusiasts.

If f'(x) is decreasing, then f”(x) is? f'(a) If f'(x) is decreasing, it means that the slope of the tangent line to the graph of f(x) is...

John Rhodes
June 21, 2023
Calculus

Discovering The Absolute Minimum Of Functions: A Guide To Calculus Critical Points And Behavior

Absolute Minimum The lowest point over the entire domain of a function or relation. The absolute minimum is the lowest possible value that a function or expression...

John Rhodes
June 21, 2023
Calculus

Discovering The Absolute Maximum Of A Function: A Guide For Calculus And Optimization

Absolute Maximum The highest point over the entire domain of a function or relation. The absolute maximum of a function is the highest value that the function...