Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Mastering The Concept Of Derivatives: A Comprehensive Guide To Calculus

Formal definition of derivative limit as h approaches 0 of [f(a+h)-f(a)]/h The derivative of a function is a mathematical concept that describes how the function changes at...

John Rhodes
June 21, 2023
Calculus

The Derivative: Definition, Interpretation, And Limit Formula

Alternate definition of derivative limit as x approaches a of [f(x)-f(a)]/(x-a) One alternate definition of derivative is the instantaneous rate of change of a function at a...

John Rhodes
June 21, 2023
Calculus

How To Understand Function Growth: When F'(X) Is Positive And Function Increases

When f ‘(x) is positive, f(x) is increasing When f ‘(x) is positive, it means that the slope of the curve of the function f(x) at the...

John Rhodes
June 21, 2023
Calculus

Why A Negative Derivative Indicates Decreasing Math Functions

When f ‘(x) is negative, f(x) is decreasing When the derivative f ‘(x) is negative, it means that the function f(x) is decreasing. Intuitively, this means that...

John Rhodes
June 21, 2023
Calculus

Local Minimum In Math: How A Change In Slope Indicates A Transition From Decreasing To Increasing Trend

When f ‘(x) changes from negative to positive, f(x) has a relative minimum local minimum. When the first derivative of a function, f'(x), changes from negative to...

John Rhodes
June 21, 2023
Calculus

Discovering Local Maximums In Math: The Relationship Between Derivatives And Function Peaks.

When f ‘(x) changes fro positive to negative, f(x) has a relative maximum local maximum at x. This statement follows from the definition of the derivative as...

John Rhodes
June 21, 2023
Calculus

Increasing F'(X): How It Affects Steepness And Rate Of Change In F(X)

When f ‘(x) is increasing, f(x) is concave up When f ‘(x) is increasing, it means that the derivative of f(x) is itself increasing, i.e., the rate...

John Rhodes
June 21, 2023
Calculus

How To Find The Derivative Of C Times U With Respect To X Using The Product Rule Of Differentiation

d/dx[cu] cu’ To find the derivative of c times u with respect to x, we can use the product rule of differentiation. Product rule states that if...