Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Mastering The Dot Product Of Matrices: The Element-Wise Multiplication And Summation For Finding A⋅B

f(x) is increasing -> f'(x) is positive positive If the function f(x) is increasing, it means that as x increases, the value of f(x) also increases. This...

John Rhodes
June 21, 2023
Calculus

Unlocking The Concept Of Positive Derivatives: The Relationship Between Function Slope And Increase In Value

f(x) is decreasing -> f'(x) is negative If f(x) is decreasing, it means that as x increases, the value of f(x) decreases. This implies that the slope...

John Rhodes
June 21, 2023
Calculus

Decreasing Functions In Calculus: The Relationship Between Slope And Derivative.

critical points f'(x) is either zero or undefined In calculus, critical points are specific points on the graph of a function where the derivative of the function...

John Rhodes
June 21, 2023
Calculus

How To Find And Analyze Critical Points In Calculus Functions

f'(x) changes from positive to negative f(x) has a relative maximum When f'(x) changes from positive to negative, it means that the slope of the function is...

John Rhodes
June 21, 2023
Calculus

Local Maximum And Minimum In Math: Explained With Examples

f'(x) changes from negative to positive f(x) has a relative minimum When the derivative of a function f(x) changes from negative to positive, it means that the...

John Rhodes
June 21, 2023
Calculus

The Significance Of Changing Derivatives: Finding Max/Min Values And Inflection Points In Functions

f”(x) is positive f'(x) is increasing and f(x) is concave up U If the second derivative, f”(x), is positive, it means that the function is concave up...

John Rhodes
June 21, 2023
Calculus

The Significance Of Positive Second Derivative In Calculus And Physics

f”(x) is negative f(x) is concave down & f'(x) is decreasing If the second derivative f”(x) is negative for a function f(x), it means that the rate...

John Rhodes
June 21, 2023
Calculus

The Significance Of A Negative Second Derivative For Concavity And Maxima Of Functions

f”(x)=0 and changes sign f'(x) has extrema and f(x) has an inflection point If f”(x) = 0 and changes sign, it means that the second derivative of...