Explain thoroughly and illustrate what it means for a function to be differentiable at a number a

Q: what is the Best use of Functions in math, also elaborates the types of function

A: Domain is defined as set of all those values of x on which function is defined while range is…

Q: How can I explain what it means for a function f(x) to be O(1)?

A: The 'f(x) to be O(1)' is to be read as function f(x) is of the order of 1.  Now refer to step two to…

Q: Suppose that f is a differentiable function satisfying the equation f(x)f(f(x))=x What is f′(1)given…

A: The given data are: f1=2f'2=3  The given equation is: fxffx=x    Differentiate both sides of the…

Q: From each corner of a square tin, 12 inches on the side, small squares of side x are removed and the…

A:

Q: How do you find the absolute extrema of a function when given the function and its interval?

A: Consider a function f(x) defined on interval [a,b] To find the absolute extrema of a given function,…

Q: Describe the x-values at which the function is differe f(x) = (x + 2)2/3

A: To describe all possible x values at which the function is differentiable.

Q: Explain and show if the function f(2) = |2|² + 2z is analytic.

A:

Q: Explain how you might differentiate a piecewise function like |x| When it's differentiable, for…

A: We can use the concept of calculus and function in order to solve the given question.

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A: A function f(x) is not differentiable at any value of x where it is not continuous.

Q: What is the purpo

A: To determine: Purpose on adding h to the function.

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A: The given function is f(x)=(x+5)23

Q: represents

A: False

Q: True or False: A function always has a point of inflection where f ″ ( x ) = 0.

A: Assume a function,

Q: Describe a procedure for finding (f ∘ g)(x). What is the name of this function?

A: Given, Describe a procedure for finding (f ∘ g)(x). What is the name of this function?

Q: Give an example to explore numerically how a function behaves near a particular point at which we…

A: Solution: Consider y = f(x) = 1/x is the function Since at x = 0, this function is going to be…

Q: How do you test a twice-differentiable function to determine where its graph is concave up or…

A: According to the Second Derivative Test for Concavity, Consider y=fx be a twice-differentiable…

Q: How does  a function behave near a particular point at which we cannotdirectly evaluate the…

A: To understand the concept we will consider an example

Q: Use the graph of the function to estimate the interval on which the function is decreasing y Enter…

A:

Q: Write an equation that expresses the fact that a function f is  continuous at the number 4.

A:

Q: Sketch the graph of a differentiable function f such that f(2) = 0, f′ < 0 for −∞ < x < 2,…

A: Given f(2) = 0, f′ < 0 for −∞ < x < 2, and f′ > 0 for 2 < x < ∞.

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A: Differentiate f(x) with respect to x

Q: You have 600 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A: Consider the dimensions of rectangle be x and y. and Perimeter of rectangle is 600 feet. we know…

Q: You have 800 feet of fencing to enclose a rectangular field. Express the area of the field, A, as a…

A:

Q: 2 -10 -8 -6 -4 -2 -2-

A:

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A:

Q: Explain the meaning of a function using a method of your choice.

A: We will find out the required solution.

Q: Describe what is the relationship between differentiability and continuity of a function.

A: To explain: The relationship between differentiability and continuity of a function. Explanation:…

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A:

Q: Investigate when, historically, the use of the function notation y=f(x) first appeared.

A: Given, Investigate when, historically, the use of the function notation y=f(x) first appeared.

Q: Explain in many ways of why an absolute value Function an piecewise Function.

A: Given:   Explain in many ways of why an absolute value Function an piecewise Function.

Q: The cost to fence in a backyard is $1000 for an area less than or equal to 100 m2. An area greater…

A: Cost function = Average cost / Area

Q: About the Discontinuity of a function, kindly provide 5 Questions about it with solutions.

A: For a function f(x) to be continuous at a point x=a, it must satisfy the two of the following…

Q: On a piece of graph paper, draw the graph of the function y equals negative 1 half x space plus…

A: The given function is y is negative one half of x and plus 1.That is y = -x/2 + 1.

Q: What is the end behavior of the function as x approaches negative infinity and positive infinity

A:

Q: Does knowing that a function ƒ(x) is differentiable at x = x0 tell you anything about the…

A: Does knowing that a function ƒ(x) is differentiable at x = x0 tell you anything about the…

Q: Distinguish the Domain in A Function f of Two Variables from Range in A Function f of Two Variables

A: Suppose the function is: f:ℝ2→ℝ2

Q: x +2 x0

A:

Q: Refer to the function:  f(x)=[x] determine f(6)

A: Given :

Q: Explain the Algebraic Function?

A: The algebraic function is defined as a function that involves only algebraic operations like…

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A: Given that  y =x2x2-4   ........... (1) At x = -2 and x= 2, y does not exist finitely  So y is not…

Q: Under what conditions imposed on functions the sum, difference, product and quotient of function…

A: We have to find the condition for which the sum, difference, product and quotient of function will…

Q: What are the steps of the procedure to find absolute extrema of a function?

A: Step 1: Find f'(x). [first derivative] Step 2: Find the critical points by solving f'(x)=0  Step 3:…

Q: Describe the x-values at which the function is differentiable.

A: The function given is y=x2x2-64. The derivative of the function y=x2x2-64. is,…

Q: Is f(x) = ±√x, a function or a relation? Give reason/s to support your answer. ( please explain in…

A: Given , function                     f(x) =±√x  Definition of function: A relation is said to be a…

Q: What is meant by a real function in reference to algebra?

A:

Q: Describe the x-values at which the function is differentiable. (Enter your answer using interval…

A:

Q: What do you mean by even and odd function? Give two examples and show by calculation that those are…

A: f is an Even Function if f(x)=f(-x) g is an odd Function if g(-x)=-g(x)

Q: 3 Can a function be always concave down and never cross zero? Can it be always concave down and…

A: The 1st answer is Yes and 2nd is No.