Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Average Rate Of Change For Calculus: Definition And Examples

Average Rate of Change of f(x) on [a,b] f'(x) = Positive The average rate of change of a function f(x) over the interval [a,b] is given by:...

John Rhodes
June 21, 2023
Calculus

Instantaneous Rate Of Change: How To Find The Slope Of A Curve At A Specific Point With Derivatives

Instantaneous Rate of Change at x=a f'(x) = Negative The instantaneous rate of change at x=a is the slope of the curve at the point x=a. It...

John Rhodes
June 21, 2023
Calculus

The Connection Between Increasing Functions And Positive Derivatives

If f(x) is increasing, then f'(x) is? f”(x) = positive If f(x) is an increasing function, then it means that as x increases, the corresponding values of...

John Rhodes
June 21, 2023
Calculus

The Relationship Between Decreasing Functions And Derivatives – Explained By A Math Expert

If f(x) is decreasing, then f'(x) is? f”(x) = negative If f(x) is a decreasing function, it means that as the input variable x increases, the output...

John Rhodes
June 21, 2023
Calculus

Concavity In Math: Positive Second Derivative And Curved Functions

If f(x) is concave up, then f”(x) is? f”(x) = positive If f(x) is concave up, then f”(x) is positive. Concave up or convexity is a property...

John Rhodes
June 21, 2023
Calculus

Concave Down Functions: Relationship Between F(X) Graph And F”(X)

If f(x) is concave down, then f”(x) is? f”(x) = negative If f(x) is concave down, it means that the graph of f(x) is curving downward or...

John Rhodes
June 21, 2023
Calculus

The Relationship Between Increasing F'(X) And Positive F”(X) – Exploring The Concave Up Graph Of F(X)

If f'(x) is increasing, then f”(x) is? y-f(a)=f'(a)(x-a) If f'(x) is increasing, then it means that the slope of the tangent line at any point on the...

John Rhodes
June 21, 2023
Calculus

Math: The Relationship Between Decreasing First Derivative And Negative Second Derivative

If f'(x) is decreasing, then f”(x) is? f'(a) If f'(x) is decreasing, it means that the rate at which the function f(x) is increasing is decreasing. In...