1. Given P(x) = x* – 8x³ + 12x2 = x2²(x – 6)(x – 2). Find the following %3D a) End Behavior b) Maximum number of local extrema. c) Zeros and their multiplicity d) Determine whether the graph crosses or touches the x-axis at each x-intercept(zero)

Q: The region between the graphs of f(x)=x^2+3 and g(x)=−x+5 has ____________area square units.

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Q: 4. Solve the following model graphically Lexicographically minimize a = {(p1 + p2), (n3). (p4), (n1…

A: The complete solutions are given below

Q: 7) A rectangle has its two lower corners on the x-axis and its two upper corners on the curve…

A: Follow the procedure given below.

Q: 4. The graph of f(x) = -3(x – 2)² – 6 is a parabola that %3D opens with its vertex at (L, ), and…

A: Given: The function fx=-3x-22-6, To determine: The given blanks in the following statement, "The…

Q: Given the functionP(x) = x – 2x +0+ A + 12 where and A are unknown 2nd and 1st order terms. The…

A: given function P(x)=x5-2x3+□+∆+12where □ and ∆ are unknown 2nd and 1st order terms.we have to find…

Q: Find the length L of the graph of 3 ( a) f(x)=x/2 +1 for 0<x< 4

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: Compare the graphs of y = Vx, y = Vx, y = x, y = x², and y x³ on the interval 0 0 and p and q are…

A: step:- 1 Generalization using nature of graph In interval (0,1) First draw graphs of x13,x12,x,x2,x3…

Q: 2. Find the critical points and determine whether they are a maximum, minimum or neither. y = a° –…

A: In the question we have to find the critical point also max. and min. points.

Q: In the function f(x) = a(x + 2)(x – 3)%, a and b are both integer constants and b is positive. If…

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Q: 4. Do you agree with the statement that " cubic functions must have at least 1 x-intercept but not…

A: 4. cubic equation must have at least 1 real solution so it must have cut the x-axis once since if…

Q: Suppose the average costs of a mining operation depend on the number of machines used, and average…

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Q: In 2009, the federal income tax T on income of x dollars (up to $82,250) was determined by the…

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Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

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Q: Find the local maximum and local minimum in (x,y) notation for the following: y=(2x2-7x)/(2x+5)

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Q: Find the values of constants a, b, and c such that the graph ofy = (x2 + a) /(bx + c) has a local…

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Q: 1. Find the maximum of P-4x+5y subject to 2x+y10 x20, y20 Sketch your feasible region and find all…

A: The LPP is given as max P=4x+5y subject to 2x+y≤24x-y≥0x+2y≥10x≥0y≥0   We will solve it by Graphical…

Q: Q2) Solve the following LP problem by graph: Maximize P = -x + 5y (x-2y ≥0 y ≤100 Subject to: x + y…

A: Given : Maximize: P = -x + 5y Subject to, x - 2y ≥ 0 y ≤ 100 x + y ≥ 210 x ≥ 0, y ≥ 0 Now, Graph :

Q: 1. The graph of f(x) = 2x3 + x² – 20x + 1 has a relative minimum at %3D A. x = -2 5 B. x = 3 C. x =…

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Q: 1. Find the absolute maximum and minimum on the given interval [1,6]. g(x) = x³ – 6x²

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Q: 9- Find the coordinates of the absolute maximum an d minimum points for f(x)=2x²-x* given x €[0,4] :

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Q: 3. The graph of f(x) = 3(x – 2)² – 6 is a parabola that opens %3D with its vertex at (L, -), and…

A: The quadratic function f(x) = a(x - h)2 + k, a not equal to zero, is said to be in standard form. If…

Q: 1. The graph of f (x) = 2x3 + x² – 20x + 1 has a relative minimum at

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Q: 1. a) Determine the coordinates of the critical points of the function y = 36x – 3x² – 2x³ b)…

A: For finding critical points  Y' = 0 For maxima and minimum values find  Y"(x1) and Y"(x2)

Q: 2- Find the value of p for which Gini's index is maximized. At which point(s) does G(p) assume its…

A: The objective is to find the value of p for which Gini's index is maximized. Also, find the points…

Q: 10. At what value of 'x' does a local maximum of y= x^3 - 3x occur?

A: We will solve the following

Q: Suppose that f ‘(x) is negative for x 1. Does f have a local minimum or maximum value at x = 1?

A: The answer is 'YES' Let see how it is YES in next step.

Q: Use the golden section method to determine with an accuracy of 0.25 the minimum of the function f(x)…

A: Let us use the golden section method to determine with an accuracy of 0.25 the minimum of the…

Q: To graph the maximum domain of the function f(x, y) = Vy – 2 - In [(y – 1)² + x – 1] The green…

A: Solve the given problem.

Q: Sketch the graph of y = (x² – 1)² – (2x – 1)². [In your answer, you must include the following: •…

A:

Q: 1. The graph of f(x) = 2x3 + x² – 20x + 1 has a relative minimum at A. x = -2 C. x = 2 D. x = 1 ק…

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

Q: of all real numbers x such that -3 < x < 5. (a) For what values of x does f have a relative maximum?…

A: at x=-3 and x=5 f is relative maximum

Q: 1) Find the Absolute Maximum and Absolute Minimum for f(x) = x³ 9x² +24x on [0,5]

A: At absolute maximum and minimum of a function y=f(x), its first derivative is zero, i.e. f'(x)=0 (a)…

Q: 1. How many point(s) of inflection are on the graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x2 -…

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Q: Suppose f:(x)=x++x³- 6r2. Determine the value of x where f has a relative minimum value. O x=2 O x=0…

A: Function f'(x)=x4+x3-6x2 To find x where f has a relative minimum value

Q: 8. (a) Use the Lagrange multiplier method to find the minimum value of among all positive x, y…

A: we need to use langrange multiplier method

Q: If f'(x) = x - 2x´ - x + 2, then ƒ has a relative minimum at x= 2

A:

Q: Find the absolute maximum and absolute minimum of  g(t) = t(square root of 4-t) on the interval…

A: Answer

Q: If f(x) = x - ka 1 has a relative maximum at r = -2, then the value of k is

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Q: From the function f(x)= x3 -6x2 +9x -3 Determines monotony, maximum and minimum points, inflection…

A: From the function fx=x3-6x2+9x-3,To determine the monotony, maximum and minimum points, inflection…

Q: 10. The function g(x) = x² − kx³ − 9x² + 7x − 8 has a minimum when x value of k. = 3. Determine the

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Q: Find the maximum value of x if f(x)=6cos(x)–3x²-2x. Using Quadratic Interpolation with a relative…

A: The function given is as follows: fx=6cosx-3x2-2x We are asked to find the maximum of the function…

Q: 1. The Maximum point of y= 9-x² x²-4

A: This is a problem related to maxima and minima. Based on the general formula and concept we will…

Q: 30. The graph of y = x³ + 21x² – x + 1 is concave down for (a) x 7 (e) x 7.

A:

Q: Sketch the following problem graphically: max f X2 = X2 subject to g1 = x1 – (1 – x2)³ < 0 92 = X1 2…

A: Given - Sketch the following problem graphically. maxx2f = x2subject to g1 = x1 - 1 - x23 ≤ 0…

Q: 8 Graphically find all optimal solutions to the follow- ing LP: min z = x1 – x2 s.t. X1 + x2 < 6 X1…

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Q: III Locate the possible y = x³ + 6x² + 9x max and min points and pt/s of inflection

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Q: For what values of a and b does f(x) = a(x- bln a) have a local minimum at the point (2, 5)? Figure…

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Q: (b) Estimate the value of x at whichf has a relative maximum. If there is no relative maximum, enter…

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Q: х — 2 Consider the function f(x) = x - 4 Use the graphing utitlity to graph f. (x- 2) (x - 4) f(x) =…

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