Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Mastering The Intermediate Value Theorem: The Fundamental Principle Of Continuous Functions On Closed Intervals

Intermediate Value Theorem Used to estimate the derivative(F(x+h)-f(x))/h The Intermediate Value Theorem is a theorem in calculus that states that if a function is continuous on a...

John Rhodes
June 21, 2023
Calculus

Optimizing Your Functions: The Importance Of The Extreme Value Theorem.

Extreme Value Theorem To find inflection points1. Find the second derivative2. Set the second derivative equal to zero3. Solve for xOptional4. Plug in and solve for f(x)...

John Rhodes
June 21, 2023
Calculus

Mastering Linear Approximation: A Fast And Accurate Way To Estimate Math Functions

Linear Approximation If f`is positive, then f(x) is increasingIf f` is negative, then f(x) is decreasing Linear approximation is a method used to estimate the value of...

John Rhodes
June 21, 2023
Calculus

Average Rate Of Change Formula For Steepness Of Math Functions

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

John Rhodes
June 21, 2023
Calculus

How To Find Instantaneous Rate Of Change At A Specific Point Using Derivatives In Math

Instantaneous Rate of Change at x=a f'(x) = Negative The instantaneous rate of change at x=a is the rate of change of a function at a specific...

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...