Give a thorough analysis of the function f(x) = x^3 / (1+x)^2 , and sketch an accurate graph of the function

Q: Express the perimeter P of a rectangle as a function of the width W if the length of the rectangle…

A: GIVENThe length of the rectangle is twice its width W

Q: Use the First Derivative Test to find any relative extrema of the function. (a) g(x) = 2x³ – 18x

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Q: The graph of which function crosses the x axis at π/2?

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Q: List the various rules that allow us to differentiate constant functions,power functions,…

A: To explain: The differentiation rule: Explanation: The constant rule is used to differentiate…

Q: How to solve functions on a graph?

A: 1st draw a graph.

Q: Describe the graph of f (x) = ex

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Q: What is the common way to obtain a new function from an existing one?

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Q: Find the derivative of the function. f(x) = 5x3 - 7x² + x %3D

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Q: Find the derivative of f(x)=2x9−x4+5

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Q: Find derivative of f(x) = (x^3-6)(x+5)

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Q: Find the relative extrema of the functions f(x)=-4x2-32x-62. Identify any maximum or minimum by…

A: Given function is Differentiating f (x) with respect to x, we get Now, we will find critical…

Q: How can the composite function be evaluated?

A: To explain how the composite function can be evaluated.

Q: Using the criterion of the first and second derivatives, find the graph of the function a) F(x) = x³…

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Q: When is a function said to have the Intermediate Value Property?

A: Let f(x) be any  function which is continuous and defined in the interval [a, b].

Q: Write cosh(ln(x)) as a rational function of x.

A: Cos h (lnx)We knowCos h (a) = ea+e-qzsoCos h (ln x ) = elnx+ e-lnx2                       = x+1x2…

Q: Use derivatives to sketch the graph of f(x) = (x² – 8x + 16)e².

A: Given

Q: 14. Use the curve sketching procedure to analyze the function. а. у-х*+x*-20х

A: since you have asked multiple questions in single request so we will be answering only first…

Q: Use the Second Derivative Test to find all relative extrema of the function f(x) = 2x - 6x +7.

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Q: sketch the graphof the function.f(x)=3^{-x^{2}}

A: we have to sketch the graph of f(x)=3^{-x^{2}}

Q: Using derivative, find the absolute maximum and minimum of f(x) = 2x3 +3x2 −12x on [−3,3]

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

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Q: Differentiate the function using any appropriate method

A: Our objective is to find the derivative.

Q: Use the first derivative test to determine the relative extreme values of the function. below. a.…

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Q: What does it mean for a function to be defined implicitly by an equation?

A: An implicitly defined function is a function that is presented as the solution of some equation or…

Q: A farmer wishes to fence the perimeter of a rectangular lot with an area of 1600 square feet. if the…

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Q: A rancher wants to fence in an area of 1,500,000 square feet in a rectangular field and then divide…

A: Let the length of the rectangular field be y and the width be x. Assume the farmer divides the field…

Q: You have 1000 feet of fencing to enclose a rectangular playground and subdivide it into two smaller…

A: The amount of fencing required would be equal to the sum of length of all the sides including the…

Q: Explain Even Functions and Odd Functions?

A: Even function: A function is even if the graph is symmetric about y axis. Or Consider f(x) is any…

Q: Find the slope of the line tangent to the graph of the function defined by f(x) = x2 – 3x + 4 at…

A: It is given that, f(x)=x2-3x+4   Slope of any function or tangent of any function is defined as the…

Q: A rancher wants to fence in an area of 500,000 square feet in a rectangular field and then divide it…

A: Let l be the length and w be the width of a rectangle.Then Area = l×b Perimeter = 2×(l+b)

Q: How would I find a function that models this?

A: From the given table , it is observed that the given table can represents a linear function.

Q: You have 1200 feet of fencing to enclose a rectangular region and subdivide it into three smaller…

A: Let  x and y be length and breadth of rectangular region respectively. Given data, Perimeter of…

Q: A farmer wishes to build a divided pasture adjacent to the river, as shown in the diagram.…

A: Let y be the side of the fence that is parallel to the border of the river side and x be the length…

Q: An open box is to be constructed by cutting out square corners of xx-inch sides from a piece of…

A:

Q: Find any relative extrema of the function f (x) = x³ - 3x². Then, sketch a graph of the function.…

A: Let f(x)= x3-3x2. We need to find the extrema of the function by using first derivative test and…

Q: How can we Represent a Function Numerically?

A: A function f from a set A to a set B is a rule that associates every member of set A a unique member…

Q: What is an even function?

A: we have to tell what is an even function.

Q: Help on identifying the parent function

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Q: How to find the derivite of a function?

A: To explain how to find derivative of function:

Q: Describe the graph of f(x) = ex

A: Given: f(x) = ex To describe: The graph of f(x) = ex

Q: Sketch the graph of fx) - x - 2x and use the graph to sketch the reciprocal function. Explain how…

A: Sketch the graph of f(x):

Q: Please

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Q: xpressed as a function of x.

A: Given,

Q: You have 600 feet of fencing to enclose a rectangular field. However, one side of the field lies…

A: To Determine: Express the area of the field, A, as a function of one of its dimensions, x. Given:…

Q: What is the definition of an even function?

A: Let f(x) be a real valued function of a real variable, then f(x) is said to be even function if…