A parabola has x-intercepts of -1, 4, Determine the equation of the parabola in f(x) = a(x-r)(x-s)  if it has a minimum value of -18.

Q: Find the values of constants a, b, and c so that the graph ofy = ax3 + bx2 + cx has a local maximum…

A: Given that: y = ax3 + bx2 + cx has a local maximum at x = 3, local minimum at x = -1, and inflection…

Q: The equation of a quartic function with x-intercepts at 1 (order 2), -3 (order 1), 2 (order 1) and…

A: Let's find.

Q: Does ƒ(x) = (7 + x)(11 - 3x) 1>3 have an absolute minimum value or an absolute maximum?

A: Here we have,  f(x)=(7+x)(11-3x)13 differentiate with respect to x

Q: Find the relative maximum point of the curve: Y=16x+4x2-x4

A: Solution of question as follows

Q: 1) Of all numbers whose difference is 2, find the two numbers that have the minimum product. [HINT:…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: The graph of f(x) = 5(x – 1)2 – 6 is a parabola that opens --Select--- , with its vertex at (x, y) =…

A: Given equation  f(x) =5x-12-6

Q: Find the absolute minimum value of the function f(x)=2ex^2-2x+1 on the domain [-1,2].

A: Given function is : fx=2 ex2-2x+1 To find the absolute minimum value of the function in the domain…

Q: Find the absolute maximum/minimum if any of f (x)=x' +3x² +1 on the interval [-3, 2].

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Q: Find global maximum and global minimum of æ3 – 9x? – 48x + 52 on the interval [-5, 12]

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Q: f(x) = x2 -x-7 is The relative maximum value of and its relative minimum value is

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Q: Find the absolute maximum value of g(x)= 2x2 −2x−2 over [0,6].

A: We have to find absolute maximum value of f(x) in given interval.F(x) is given as:

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: At which value does the function g(x)= 3x^4 - 4x^3 attain a minimum and what is the minimum value?…

A: Sol:- Suppose that x=c is a critical point of fx then, If f 'x<0 to the left of x=c and f 'x>…

Q: find constants a and b so that the minimum for the parabola f(x)=x2+ax+b is at the point (6,7)

A: Minimum for function can be found using second derivative test

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: Find the absolute extremd of the on the closed interval. 6x2 g(x) (-2, 1) X - 2 minimum (x, y)…

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Q: Does x=6 belong to a local maximum or a local minimum? Does x=0 belong to a local maximum or a local…

A: Here we have,  differentiate with respect to x

Q: Give the domain and range of the quadratic function whose graph is described. Minimum = - 7 at x = 1

A: The solution is attached below in Step 2

Q: Find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cx has a local…

A: We have to find the values of constants a, b, and c such that the graph of y = ax3 + bx2 + cxhas a…

Q: Y=24x^3-3x^4 = x^3(24-3x) What are the local and absolute maximum/ minimum and their coordinates

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Q: 7. Find the absolute maximum and the absolute minimum off(x) = 2x³ – 3x - 12x + 5 on the interval…

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Q: Let f (x) be the square of the distance from the point (2, 1) to a point (x, 3x + 2) on the line y =…

A: The square of the distance between two points (a, b) and (c, d) = (c - a)2 + (d - b)2

Q: Find the relative maxima or minima. Maximum of ƒ(x, y) = x2 - 5y2, subject to x - y = 12

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Q: Rx) =-x + 6x + 5 on [5, 8] maximum minimum

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Q: Find constants a and b so that the minimum for the parabola f (x) = x² + ax + b is at the point (4,…

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Q: The function Ax) = -2x(x - 1)(x - 2)(x+ 2) %3D has 4 zeros. has a maximum O as x→-∞, y–-∞ all of the…

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Q: Determine the values of constants a and b so that ƒ(x) = ax2 + bx has an absolute maximum at the…

A: Given:

Q: 1. Find the absolute maximum and minimum of y = x³-3x² + 2, [-1, 3]. Sketch the graph.

A: Given function is y=x3-3x2+2

Q: Find the absolute minimum and absolute maximum for y = x3 – -+ 4x +1 on [-2,2].

A:

Q: A rectangle has its two lower corners on the x-axis and its two upper corners on the curve y = 16 -…

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Q: Find a quadratic function f (x) = ax2 + bx + c which has a vertex at (1, 1) and passes through (3,…

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Q: Do you agree with this statement. Cubic functions must have at least one x intercept but not more…

A: Given statement : Cubic functions must have at least one x intercept but not more than 3 whereas…

Q: 2) Find the equation of a quadratic function with a maximum value at (2,5) and a vertical intercept…

A: We have to find equation

Q: Let a be a real number and a and B the roots of x'- 2a'x+1= 0. Show that attains a' a minimum…

A:

Q: Express y = 3x2 – 8x - 1 in the form y = 3(x – p)² + q, where p and q are constants and hence find…

A: To express in the form y=3(x-p)²+q

Q: Find the absolute meximum and absolul-e minimum of fcx) = X intereval [4,8] x- 48X Over the

A: From the given function; fx=x33+x2-48x First, we have to find the critical points; As we know that,…

Q: Find the minimum absolute extremum as well as all values of x where it occurs on the specified…

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Q: 1. Find the maximum point of the following curve. <press your answer in this form (#,#) or N/A if…

A: Differentiate the given function with respect to x and then solve y'= 0 to obtain the critical…

Q: Find the values of constants a, b, and c so that the graph of y = ax3 + bx2 + cx has a local maximum…

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Q: f(x) = -x + 6x + 5 on [5, 8] %3D maximum minimum

A: Differentiate wrt x and put derivative to zero for maxima and minima  If value of x lies on given…

Q: What is the absolute minimum value of q(x) = 2x -1 over -2, 5?

A: We have to find the absolute minimum value of q(x) = 2x2 - 1 over [-2, 5].

Q: The minimum v value of this quadratic function is 0 v At the point ( ), the x-axis intercepts with…

A: We use the data from the graph to complete the sentences. The minimum value of this quadratic…

Q: graph of f(x) = 4(x – 2)² – 7 is a parabola that opens --Select- v with its vertex at (x, y) = ( and…

A:

Q: Find the minimum distance from the parabola x-y2=0 to the point (0,3)(0,3).

A: Given data:   The given expression for the parabola is x-y2=0. The given point is (x1, y1)=(0,3).…

Q: (4,28) is a maximum or a minimum point of the function g(x) = -x3 + 6x? – 4. Verify whether the…

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

A: