Calculus | Senioritis

John Rhodes
June 21, 2023
Calculus

Implicit Relations In Mathematics: Definition, Examples, And Applications

Implicit Relations if f’=0 or f’ DNE –> critical pointif f”>0 concave up An implicit relation is a mathematical equation in which the dependent variable is not...

John Rhodes
June 21, 2023
Calculus

Guide To Determining Concavity With Second Derivative: Step-By-Step Explanation.

Determine Concavity f is concave up: f’ is increasing: f” > 0 (positive)f is concave down: f’ is decreasing: f” < 0 (negative) Concavity is a term...

John Rhodes
June 21, 2023
Calculus

Mastering Curve Sketching: A Guide To Consider Domain, Symmetry, Critical Points, Concavity And More

Determine Function Behavior (Curve Sketching) 1. find critical points (y’=0 or y’ DNE)2. test the regions to see if function incr or decr3. find possible inflection points...

John Rhodes
June 21, 2023
Calculus

Ensuring Well-Defined Compositions: Domain Restrictions In Function Composition – A Math Perspective

When we compose functions, we must make sure that the output of the first function is part of the ___ of the second function. domain When we...

John Rhodes
June 21, 2023
Calculus

Why The Composition Of Functions Is Not Commutative: The Basics Of Function Composition

In general, the composition of functions is not ___. commutative In general, the composition of functions is not commutative. The composition of functions is a binary operation...

John Rhodes
June 21, 2023
Calculus

Exploring The Line Of Symmetry: The Graph Of A Function And Its Inverse Composition

We expect to see a ___ for the graph of a composition of a function and its inverse function, if the domain of each is all real...

John Rhodes
June 21, 2023
Calculus

Unlocking The Mystery Of Function Composition: A Step-By-Step Guide With Examples

Find the composition of the function.g(x)=sqrt(x) and g(x)=sqrt(x) find f(g(x)). x^(1/6) To find the composition of the two functions, we can substitute g(x) into f(x), which gives...

John Rhodes
June 21, 2023
Calculus

Discover The Compositional Rule Of Functions With An Example: F(X) = X^(1/3) And G(X) = X

Find the composition of the function.f(x)=x^1/3 and g(x)=x Find g(f(x)). x^(1/6) To find g(f(x)), we first need to express f(x) in terms of x and then substitute...