Calculus | Senioritis

John Rhodes
July 29, 2023
Calculus

Understanding the Implications of f'(x) = 0 | Horizontal Tangent Lines and Local Extrema in Math Functions

if f'(x) is EQUAL to 0, then f is _____ on (a,b) If f'(x) is equal to 0, this means that the derivative of the function f(x)...

John Rhodes
July 29, 2023
Calculus

Understanding Decreasing Functions | The Relationship Between f'(x) and f(x)

if f'(x) is LESS than 0, then f is _____ on (a,b) If f'(x) is less than 0, it means that the derivative of the function f(x)...

John Rhodes
July 29, 2023
Calculus

Understanding Increasing Functions | The Relationship between f'(x) and the Increase in f(x)

if f'(x) is GREATER than 0, then f is _____ on (a,b) If f'(x) is greater than 0 on the interval (a,b), it means that the derivative...

John Rhodes
July 29, 2023
Calculus

Understanding Intervals of Increase and Decrease | Analyzing Math Functions Based on x-Values or the Domain

intervals of increase and decrease are listed in terms of the ____ Intervals of increase and decrease are listed in terms of the x-values or the domain...

John Rhodes
July 29, 2023
Calculus

Understanding Rightward Shifting Functions | How Graphs Move to the Right as x Increases

a function is ____ if its graph moves ____ as x moves to the right A function is called a “rightward shifting” function if its graph moves...

John Rhodes
July 29, 2023
Calculus

How to Solve the Integral ∫-1/(x√x^2-1) dx with Step-by-Step Explanation

∫-1/(x√x^2-1) dx To solve the integral ∫-1/(x√x^2-1) dx, we can begin by making a u-substitution to simplify the expression To solve the integral ∫-1/(x√x^2-1) dx, we can...

John Rhodes
July 29, 2023
Calculus

How to Evaluate the Integral of sin x with Respect to x

∫ sin x dx The integral of sin x with respect to x can be evaluated as follows: ∫ sin x dx = – cos x +...

John Rhodes
July 29, 2023
Calculus

Mastering Integration | The Integral of Cos(x) and Constant of Integration Explained

∫ cos x dx To find the integral of cos(x) with respect to x, we can use the basic rules of integration To find the integral of...