Use the first-derivative test to determine the local extrema of the function f. Then verify your algebraic answers with graphs from a calculator or graphing utility. (Enter your answers as comma-separated lists. If an answer does not exist, enter DNE.) 4 + x + x2 f(x) = x² + x - 2 local maxima X = local minima X =

Q: Let f(x) = x² – 8x – 14 Use the second derivative test to find any local maxima and minima. First,…

A: for critical value put first derivative zero if second derivative positive minima and if negative…

Q: Given the derivative f′(x), find the x-value for all relative extrema for the graph of the original…

A: Answer

Q: Given the function g(x) = 8x° – 60x + 96x, find the first derivative, g'(x). g'(x) = Notice that…

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Q: Locate the critical points of the following function. Then use the Second Derivative Test to…

A: Given Data The function is h(x)=(x+a)4.   Differentiate the function h(x)=(x+a)4 with respect to x…

Q: For the function, find all critical numbers and then use the second-derivative test to determine…

A: We use the power rule to find f'(x) and f"(x) f(x)=x4-4x3+4x2+3f'(x)=4x3-12x2+8xf"(x)=12x2-24x+8…

Q: Suppose a tour guide has a bus that holds a maximum of 86 people. Assume his profit (in dollars) for…

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Q: Consider the function g(x) = (x^4) + (6x^2) +17. Locate and classify all relative minima and maxima.…

A: Given that g(x)  = x4 + 6x2 +17 find local minima and maxima. Here i attached solution of this…

Q: Locate the critical points of the following function. Then use the Second Derivative Test to…

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Q: Use the first & second derivatives to answer the following questions: What are the critical points…

A: To Determine: a) find first and second derivatives b) what are the critical points of f ? c) where…

Q: For the function y= x² -8x +20 a. Determine the critical points  b. Use the sign test to classify…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

A: Differentiate the function fx=xx2+1 with respect to x, to obtain f'(x) and f''(x).…

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: Use the definition of a derivative to find f (x) and f"(x). f(x) - 3x2 + 9x + 1 f(x) - F"(x) = Graph…

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Q: Use the second derivative test to find the relative extrema of the following function. Make sure to…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Which of the following are local extrema (local maxima and local minima) of the function f(x)?

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Q: Given f(x) = - x² – 3x + 2, a) Use the second derivative test to classify the local extrema of f(x).…

A: We use second derivative test in part a to find local maximum and minimum  for absolute maximum and…

Q: Given the derivative f'(x), find the x-value for all relative extrema for the graph of the original…

A: Consider the given derivative. f'x=x2−5x+6 Put the first derivative equal to zero.…

Q: Two business students at Brock University decided to open a small company together to sell their own…

A: Given query is to find the the correct option for rthe graph of f(x).

Q: (A) Find the absolute maxima and minima for ,3 Y = x + 5 over [-V2, v2). (B) Use the second…

A: y = x33-x+5y' = 3x23-1y' = x2 -1x2-1 = 0x2 = 1x = ±1

Q: For the function, find all critical numbers and then use the second-derivative test to determine…

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Q: Consider the following function. g(x) = 2x2 + 32/x + 12

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Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: Given the function g(x) = 8x° - 84x + 288x, find the first derivative, g'(x). g'(x) = Notice that…

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Q: Use the second derivative test to find the values of x where f(x) has local maximum or local minimum…

A: Consider the given function f(x)=cos(3x), x∈[-π/6, π/6]

Q: Two business students at Brock University decided to open a small company together to sell their own…

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Q: Consider the function h(x) = x' – 4x° + 10. Use the second derivative test to find the x-coordinates…

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Q: a)Use the second derivative test to determine whether the function has a local maximum or local…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

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Q: 1. Sketch the graph of the function 4x f(x) = x E (-00, 00) 1+4x² Be sure to calculate the local…

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Q: For each function, perform the following steps: i. Find any critical points ii. use the first…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

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

A: To find relative extremas first we need to find critical points. These are the points where first…

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

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Q: b. Use the Second Derivative Test to find all local minima and local maxima for g(x).

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Q: Locate the critical points of the following function. Then use the Second Derivative Test to…

A: Given function is fx=x44-5x33-4x2+48x. For critical points we need to find first derivative of…

Q: Use the first & second derivatives to answer the following questions: What are the critical points…

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Q: Use calculus techniques to establish the first and second derivatives of the following functions and…

A: (a) Given information: The function is f(x)=x2x+1. 1) To find: The points where f(x) = 0. Solution:…

Q: For the function, find all critical numbers and then use the second-derivative test to determine…

A: we have to find the critical points and relative maxima and minima at

Q: Find the local maximum value of f using both the First and Second Derivative Tests. (If an answer…

A: Given fx=x+5-x

Q: Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that…

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Q: Consider the following function. 9(x) = x + 3x2- 8 on [-3, 1] Find the derivative of the function.…

A: Since, we have been given that g(x)=x3+3x2-8 on -3,1(a) Our Aim is to find the derivative of the…

Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: f(x,y)=x2+y2-2x+17Now, dfdx=2x-2x2+y2-2x+17dfdx=2yx2+y2-2x+17for critical point…

Q: 13. Suppose f is a function whose first derivative is f'(x) = 1(x+1)(z-1)2(z-2). Sketch a sign chart…

A: Local maxima and minima

Q: Let f be a function with first derivative given by f' (x) = (x + 1)(x – 2)(x – 3). At what values of…

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Q: The function f(x) = 6x + 8x has one local minimum and one local maximum. Algebraically use the…

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Q: Find the values of x for which f (defined below) has a horizontal tangent line f(x)=(1/3)x3…

A: To Find the values of x for which f(x) has a horizontal tangent line f(x)=(1/3)x3 -(1/2)x2 -6x+7…

Q: For the function, find all critical numbers and then use the second-derivative test to determine…

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Q: Consider the following function. g(x) = x2 - 2x - 6 on [0, 8] Find the derivative of the function. 9…

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Q: 5. Let f(x) = 5x4 - -2+8√√x-3. (a) Find f'(x). (b) Find an equation for the tangent line to the…

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Q: Find the relative extrema of the function, if they exist. Use the First Derivative Test to state if…

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Q: Consider the function h(x) = ((x^2) - x) / ((x + 1)^2), which has first derivative h'(x) = (3x - 1)…

A: To find the vertical asymptotes, locate and classify all relative minima and maxima and point(s) of…