1. Consider the following function: f (x) 2x2 – x4 A. Find the critical values. B. Use the "Second Derivative Test" to determine which points the local minimum and local maximum occur at. C. What are the points of inflection, if any?

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Q: Q1) The dervative of the function f(x)= |x+2, using the definition of derivative is 1 b)- a) x+2 x+2

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Q: 8. Suppose the derivative of the function y = f(x) is y' = (x – 1)*(x – 2)(x – 4). At what points,…

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Q: • Show that both of the functions f(x) = (x − 1)^4 and g(x) = x^3 −3x^2 + 3x+ 2 have stationary…

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Q: 1. Find the derivative function for the following using the power rule: a) f(x) = x¹² b) y = 8x³ -…

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Q: Use the graph of the first derivative function f'(x) to find x values at which function has relative…

A: First of all, consider the graph of f '(x).

Q: 4. Given f (x )=x'-12x +1. Use the second derivative test to determine the local extremum off (x).

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

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

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A: To find f(x+h) replace x by x+h in f(x).

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A: (a) For critical points:

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Q: Answer the following questions about the function whose derivative is f'(x) = (x-8) (x + 9). a. What…

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Q: 1. Find and classify all critical points of the following function: f(x, y) = x* + 2y² – 4ry

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A: Given equation of derivative,  f'(x) = x-1/5(x-4)    For part A).  f'(x) = 0 x= 0 and 4 are critical…

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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Q: 1. Determine the third derivative of the following. A. f(x) = x³ – 4x² + 5x + 3 B. f(x) = Inx [ K:…

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Q: 1. Use the definition of derivative to find f'(1) 2r2 b) f(x) = Vx

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

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Q: 3- Suppose that the second derivative of the function y = f(x) is y" = (x + 1)(x - 2). For what…

A: 1)y'' = (x+1)(x-2)2)y' = (x-1)2(x-2)(x-4)

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Q: 8 x - y a(x, y)

A: Given :- The given multivariable function is ax,y = 8x-yex2 +y2. To determine :- The critical points…

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