Question Given q(x) = x* – 4x² + 10, find the x-coordinates of all local minima. If there are multiple values, give them separated by commas. Enter them as exact answers.lf there are no local minima, enter Ø. Write an exact answer, do not round.

Q: A quadratic polynomial y = 4x2 +7x -3 has roots p and q. Find a quadratic g(x) = x² + ax +B with…

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Q: 3. The diagram on the right shows an open box with a square base of side x cm and a height of h cm.…

A: This is problem of optimization and application of differential calculus.

Q: Let f(x) = 9x2 (x – 7) + 9. Find the critical points c that correspond to local minima. (Use…

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Q: Find the maximum value of f(x, y) = 6x²y3 +5 on the unit circle. Give an exact answer. Use symbolic…

A: solution :-

Q: Find all zeros of f(x) = 4x° + 4x-17z + 21. Enter the zeros separated by commas. Enter exact value,…

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Q: f(x) = 2x2 + 32x + 126 (a) Express f in standard form. f(x) %3D (b) Find the vertex and x- and…

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Q: Find all points of discontinuity. x² + 4x +4 f(x) = x2 +x-6 Select the correct choice below and, if…

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Q: 2. For the function g(x) = -2x² a. vertex b. axis of symmetry c. root(s) ototion

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: 16 Diberi fungsi k : x → 3x – 9, cari Given the function k : x→ 3x – 9, find (a) k-1(x), - 17

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Q: Solve the inequalities. Express the solution sets asintervals or unions of intervals and show them…

A: Solve the inequality: x2-x<0

Q: Minimum-perimeter rectangles Of all rectangles with a fixedarea A, which one has the minimum…

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Q: Let f(x) = 10x²(x-7) +4. Find the critical points c that correspond to local minima. (Use symbolic…

A: Given function is f(x)=10x2(x-7)+4

Q: 1. Find the coordinates of the vertex of the given function using two methods: a) Completing the…

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Q: Let f(x) = 9x²(x-7) + 1. Find the critical points c that correspond to local minima. (Use symbolic…

A: Given  function is f(x)=9x2(x-7)+1 The critical points of a function are the points where f'(x) is 0…

Q: Find all points of discontinuity. f(x) = + 4x + 4 x²+x-6 2 Select the correct choice below and, if…

A: We can find discontinuity .

Q: Find the maximum of f(x, y) = 3y² + 5xy – 3x² on the square domain 0 < x < 6,0 < y < 6. (Give an…

A: Given: f(x,y)=3y2+5xy-3x2

Q: Using Lagrange's interpolation formula to fit a polynomial to the data -10 2 3 BBBBH y -83 1 12 And…

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Q: A quadratic polynomial y = 4x² + 7x – 3 has roots p and q. Find a quadratic g(x) = x² + ax + ß with…

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Q: X in c) Find the x-value that gives the maximum perimeter over all such rectangles. (Don't forget to…

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Q: OOOO y= 4x -8x+c, lsrs2] y=-5x +b,x- 27 2sxs3 S(x) = calculate the value of es assoming contuuity of…

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Q: 3+ x2 ' Find the vertices of the rectangle with maximum area. Vertices = Enter your answers as a…

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Q: 4. A box constructed from a rectangular paper has a volume of not more than 180 cubic cm. If the box…

A: Solved below

Q: Find the maximum of f(x, y) = 3y² + 5xy – 3x² on the square domain 0 < x < 6, 0 < y < 6. %3D (Give…

A: f(x,y)=3y2+5xy-3x2 To find out maximum , we take derivative with respect to x  and y…

Q: Find positive numbers x and y such that x + y = 63 and 2xy is maximized. Select the correct choice…

A: Use applications of derivative

Q: A rectangular garden consists of a rectangular lawn of area 72m2. The pass is 2m wide at two longer…

A: We use second derivative test to find out where area is minimum

Q: y = -x^3+6x^2+63x-100 Find and show work - Local maxima = ? Local minima = ? Inflection Points =

A: Given:y=-x3+6x2+63x-100y=x3-6x2-63x+100Local maxima d2ydx2&lt;0Local minima d2ydx2&gt;0Point of…

Q: A. Fiil in the boxes by following the steps found on the right side 1. f(x) = 3x² – 4x + 1 = O&² -…

A: The  given equations are,1. f(x)=3x2-4x+12. y=x2-4x-10

Q: 4) f (x) = x°+6x+9x+3 Clossify whetn + these antical (D.) Find the points of inflechon If there are…

A: Given f(x)=x3+6x2+9x+3

Q: Find the maximum of f(x, y) = 3y + 3xy – 3x² on the square domain 0 < x < 4, 0 < y < 4. (Give an…

A: Complete the square:  fx,y=3y2+3xy-3x2         =3y2+3×y22-3×y22+3xy-3x2…

Q: O g(x) = -6(x – 2)2(x + 1)3 O Degree: O End Behavior: O How many zeros? O What are the zeros…

A: As per bartleby guidelines, I need to answer only 3 sub-parts of a question. So, you can post the…

Q: Find the maximum of f (x, y) = 3y + 4xy – 3x on the square domain 0 < x < 9, 0 < y< 9. (Give an…

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Q: Find the length of the curve x = 30 * 2y on 3sys 5. The length of the curve x =- (Type an integer or…

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Q: Integers a and b are such that (a + 3-5) +a- brS = 51. Find the possible values of a and the…

A: Given integers a and b such that a+352+a-b5=51

Q: A quadratic polynomial y = 4x² +7x-3 has roots p and q. Find a quadratic g(x) = x + ax +B with roots…

A: Use the given conditions.

Q: A quadratic function is given. f(x) -x2 + 10x + 5 (a) Express the quadratic function in standard…

A: See the attachment

Q: Find the maximum value of f(x, y) = 2x²y³ +5 on the unit circle. (Give an exact answer. Use symbolic…

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Q: A quadratic function f is given. f(x) = 2x2 + 12x + 10 (a) Express f in standard form. f(x) = (b)…

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Q: A gardener will use up to 240square feet for planting flowers and vegetables. He wants the area used…

A: Area used by the gardener for planting flowers and vegetables is 240 square feet. The area used for…

Q: The revenue (R) from the number of sales (x) of a certain videogame is described by the functi R(x)…

A: Given revenue function R(x)=-0.14x2+420x to maximize it lets use double derivative test.

Q: 3. Determine g'(1) for g(x) = (8x² – 3x)³. -

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Q: f(x) = -8x2 + 1 has a: %3D O minimum O neither a minimum or maximum O maximum

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Q: Find the maximum value of f(x, y) = 6x²y³ + 5 on the unit circle. (Give an exact answer. Use…

A: In mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local…

Q: Find all points of discontinuity f(x)= x + 4x + 4 x²+x-6 ... Select the correct choice below and, if…

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Q: A quadratic polynomial y = 4x2 +7x – 3 has roots p and q. Find a quadratic g(x) = x² + ax + ß with…

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Q: A cubic function is a polynomial of degree 3; that is, it has the form f(x) ax3 + bx? + cx + d,…

A: f(x) = ax3 + bx2 + cx + d on differentiating, f '(x) = 3ax2 + 2bx +c which is a quadratic in x and…

Q: Find the zeros of the function and state the multiplicities. m (x) = -4x (x– 1)°(x+2)² If there is…

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Q: General quartic Show that the general quartic (fourth-degree)polynomial f(x) = x 4 + ax 3 + bx 2 +…

A: Inflection points are those points where the second derivative of a function is zero. To find the…

Q: Find the maximum value of f(x, y) = 2x²y³ + 7 on the unit circle. (Give an exact answer. Use…

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Q: (2 points) Consider the Quadratic function f(x) = 2x² – 15x – 8. Its vertex is ( ); its x-intercepts…

A: A quadratic function is a function that can be written in the form f(x)=ax2+bx+c, where a,b, and c…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.