Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

How Rolle’S Theorem Helps Find Horizontal Tangents And Multiple Roots Of Polynomial Equations In Calculus

Rolle’s Theorem if f(x) is continuous on [a,b] and differentiable on (a,b), and if f(a)=f(b), then there is at least one point (x=c) on (a,b) where f'(c)=0...

John Rhodes
June 21, 2023
Calculus

The Power Of Mean Value Theorem In Calculus Optimization: Finding Critical Points And Extrema

Mean Value Theorem if f(x) is continuous on [a,b] and differentiable on (a,b), there is at least one point (x=c) where f'(c)= f(b)-f(a)/b-a The Mean Value Theorem...

John Rhodes
June 21, 2023
Calculus

Increasing Functions: Explained With Slopes And Derivatives

f(x) is increasing when f’ > 0 A function, f(x), is said to be increasing if its values increase as the input variable x increases, or in...

John Rhodes
June 21, 2023
Calculus

How To Determine If A Function Is Decreasing: A Guide To Calculus.

f(x) is decreasing when f’ < 0 In calculus, a function f(x) is decreasing if its values are decreasing as x increases. This means that if we...

John Rhodes
June 21, 2023
Calculus

Critical Points In Calculus: Identifying Local Extremes And Inflection Points

f(x) has a critical point when f’ = 0, f’ is undefined A critical point of a function f(x) is a point x=c where the derivative of...

John Rhodes
June 21, 2023
Calculus

Mastering Concavity Of Functions: Analyzing Derivatives For Peak Performance

f(x) is concave up when f’ is ____ or f” is ____ increasing, f” > 0 To determine the concavity of a function, we need to analyze...

John Rhodes
June 21, 2023
Calculus

Mastering Concave Down Functions: Using The Second Derivative And Slope Of The First Derivative To Evaluate F(X)

f(x) is concave down when f’ is ____ or f” is ____ decreasing, f” < 0 To determine whether f(x) is concave down, we can look at...

John Rhodes
June 21, 2023
Calculus

Discovering Inflection Points In Math: The Significance Of F”(C) Changes

f(x) has an inflection point at (c, f(c)) when the concavity changes at f”(c) = 0 or f”(c) is undefined f”(c) changes sign at point c. In...