For the function f (x) answer the %3D 1+ x3 following question, a) Determine the open intervals on which the function is concave up and concave down, search an inflection point if it is exists.

Q: Given f (x) =x-4 and g (x)=|x+2|, what is the domain of the quotient function f/g?

A: Domain will be  Whole real numbers except 2 Explanation is given below......

Q: Consider the function below. List the answers. x2 + 3x – 40 f(x) = x2 – 6x + 5 - For what real…

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Q: Find the intervals in which the function f(x) = x4 – 8x3 – 5 is concave up/concave down. Also find…

A: From the given problem:   fx=y=x4-8x3-5   As we know that:   a). For concave upward f''x or…

Q: Use the graph to estimate the open intervals on which the function is increasing or decreasing. Then…

A: From the given graph we see that the vertex is at (3,-1)  So, up to x=3, the function was…

Q: Given the function f(x) = x* – 24x², determine all intervals on which f is both decreasing and…

A: For any function in interval a,b if f'(x)<0, then f(x) is decreasing in the interval a,b and…

Q: Given the function f(x) = 2x + 6x?, determine all intervals on which f is both decreasing and…

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Q: For the function f (x) = 2-x² – x² +x, (a) List the x values where = 0. (b) Are all of these values…

A: Consider the given function, f(x)=2x4-x2+x Find the first derivative of the given function,…

Q: For the real-valued functions g(x)=x^2+2 and h(x)=x^2+4, find the composition g of h and specify its…

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Q: Given the function f(x) = –6x4 + 36x², determine all intervals on which f is %3D both increasing and…

A: Given: f(x) = -644 + 3642   for critical points  f'(x)= 0 so,…

Q: Consider the function below.f(x) = 1 + 3x^4 − 2x^5(a) Using analytical methods, find the intervals…

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Q: Given the function f(x) = -6xt + 36x2, determine all intervals on which f is both increasing and…

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Q: Given the function f(x) = 2x +36x² – 78x, determine all intervals on which f is both increasing and…

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Q: Given the following function f(x)=3x5-20x3, find the following: The x-intervals where f(x) is…

A: For point of inflection f"(x)=0

Q: Use the given graph of the function to find the a-values for which f is not differentiable. Answer…

A: Graph of the function is given, we have to find the points for which f is not differentiable.

Q: Consider the graph of f(x) below. Over what open interval is f'(x) positive? Give your answer in…

A: Given: The graph of the function f(x) is shown as: To find: The open interval where f'(x) is…

Q: Q1: - Find C that make the function f(x) continuous f(x) = {| x +3 Сх+ 6 x 2

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Q: Consider the function below. f(x) = Vx - 16x + 48 %3D What is the Domain? Enter your answer in…

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Q: Let f(x) = V12 – æ and g(x) = æ² – x. - What will be the domain of the composite function, fog ? The…

A: Let A,B and C be two non-empty sets, a function f:A→B and g:B→c, the composition of f and g is…

Q: Determine whether  the following statement is true or false, and explain why. If ƒ″(c) = 0, the…

A: The given statement is true.

Q: Given the function f(x) = 2x + 16x° + 36x, determine all intervals on which f is both increasing and…

A: f(x) is both increasing and concave up in interval from 0 to infinity...as I have done solution in…

Q: (b) Find the intervals in which the function f (x)=x* +6x' +6 is concave up/concave down. Also find…

A: When f''>0 then function cancave up when f''<0 then function cancave down

Q: Given the function f(x) = –6x + 36x², determine all intervals on which f is both increasing and…

A: Given the function  f(x)=-6x4+36x2

Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: Determine where the function is concave upward and where it is concave downward. (Enter your answer…

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Q: Consider the following functions: f(x)= x+1' and g(x) = Find the domain of (f og)(x). Enter your…

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Q: Given the function f(x) = -x + 5x4, determine all intervals on which f is both increasing and…

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Q: Find the open interval(s) of f(x), graph given below, where f'(x) is positive.

A: Given: The graph of the function f(x) is shown as: To find: The open interval of f(x) where f'(x)…

Q: Use the graph of the function y=f(x) below to answer the questions. y 5- # 3- 2+ 1- -5 -4 -3 -2 -1 4…

A: The given graph is:

Q: Given the function f(x) - xer, Determine the open interval(s) where the function is concave up…

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Q: 4. If f(x) = ax' +bx', determine a and b so that the graph of f will have a point of inflection at…

A: we need to determine the values of a and b.

Q: Use the graph of the function y=f(x) below to answer the questions. -3 (a) Is f(3) positive? (0,0)…

A: This is a problem of function f(x). Graph is given for f(x) and in context to that graph we will…

Q: For the given function, where is it concave up and concave down? Give your answers in interval…

A: Concavity of the function using second derivativetest

Q: Consider the function below. List the answers. x2 + 9x + 14 f(x) x2 + x – 2 For what real numbers is…

A: A rational function is discontinuous at the points on which the denominator is zero.

Q: The domain of the function f(x)= sech( -8) is ( 160, A], Then The value of k = %3D

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Q: For the given function, where is it concave up and concave down? Give your answers in interval…

A: h'(x)=2(e^(-3x) -3xe^(-3x)) h"(x)=2(-6e^(-3x) +9xe^(-3x)) h"(x)=0 2(-6e^(-3x)+9xe^(-3x))=0 -6+9x=0…

Q: Does the test function satisfy the conditions of Rolle's theorem on a given interval? If satisfied,…

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Q: Show that if f(x)  = x4 , then  f"(0)  =0, but  (0, 0)is not aninflection point of the graph of f.

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Q: Consider the function below. List the answers. x2 – x – 20 - f(x) x2 – 25 - For what real numbers is…

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Q: For f(x)=1/1-x, find f(f(x)) and f(f(f(x))) (show work)

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Q: Given that f(x) = 5x – 13 where f(x) = y, define a function rule for f-1.

A: Given function, fx=5x-13 The objective is to find the inverse function. y=fx⇒f-1y=x The following…

Q: Use the given graph of the function to find the x-values for which f is discontinuous. Answer…

A: Graph of function is

Q: The function f(x)%= has a point of inflection when a = 0.

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Q: (b) Find the intervals in which the function f(x)=x* +4x'+7 is concave up/concave down. Also find…

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Q: Given the function f(x) = -x³ + 5x*, determine all intervals on which f is both increasing and…

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Q: Find all values of x such that f (x) > 0 and all x such that f (x) < 0, and sketch the graph…

A: Given function is, fx=-x4+12x2-27. It is factorize as follows:…

Q: Given the function f(x) = - x6 + 2x° – 5x², find all intervals on which f is concave down.

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.