Consider the Quadratic function f(x) = 9z? – 1. - Its vertex is ). The x value of its largest x-intercept is x = The y value of the y-intercept is y =

Q: Find the mioimum and maximum values of the function subject to the gicen fCx.y)=6x?+Sy? 3X+10y=3

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Q: 1. For the quadratic function f(x) = x² + 6x + 11: a) Write the function in the form f(x) = a(x –…

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Q: Find the maximum and minimum value of f(x,y) =x3+3xy2-3x2-3y2+4

A: fx,y=x3+3xy2-3x2-3y2+4   fx=3x2+3y2-6x   fxx=6x-6   fxy=6y   fy=6xy-6y   fyy=6x-6

Q: For the function y = -2+5 sin (x-2), what is the maximum value?

A: Given,Function y =-2+5sinπ12(x-2)

Q: Find the quadratic function f(x) = ax + bx +c that goes through (2,0) and has a local minimum at (0,…

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Q: Determine two positive numbers e and f whose product is 27 and for which the value of 4f +3e is a…

A: Product is 27 and 4f+3e is a minimum.

Q: Determine the equation of the quartic function with the following characteristics x-intercepts at x…

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Q: Given U = VXY; and Px=10 , Py-20, income=100; what is the value of MRSxy at the optimization point?…

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Q: 3. If y = 4v2 r x – 1, find the length of the graph of f 3 from point a = 0 to x = 1.

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Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: Suppose that f(æ, y) = e-3x² – 4y? + y Then the maximum is

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Q: If k = 3, for approximately what values of x in the interval [0, 1] will the error in the quadratic…

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Q: Find the point on the parabola x = t, y = t2, -infinity<=t <=infinity, closest to the point…

A: Consider the required point as (x,y)Consider the formula of distance between the two points.

Q: Find all points (x, y) on the graph of g(x) = 1/3 x3 - 3/2 x2 + 1 withtangent lines parallel to the…

A: Given: The function gx=x33-3x22+1, To find: All the points x,y on the graph of given function at…

Q: Write the general solution of the fourth-order DE y(4) – 2y" + y = 0 entirely in terms of hyperbolic…

A: We have to find the general solution of the differential equation y4-2y''+y=0. The auxiliary…

Q: You will calculate L5 and U5 for the quadratic function y 2² + z + 14 between z = 0 and z = 2. Enter…

A: To solve the following problem

Q: 27The platis that passes through the e Point C672) and contains the lihie メー4-2t)X= 345t) Zと+4t 4. こ

A: We have to find the equation of the plane which passes through the given point and contains the…

Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum.

A: To solve the following problem

Q: 3. The cost, c(x), in dollars per hour of running a certain steamboat is modelled by the function…

A: Detailed explanation mentioned below

Q: For the function f(x) = x³ – 27x, its local maximum is which occurs at ( its local minimum is which…

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Q: A company with a monopoly is able to control the price of its product by limiting supply. If the…

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Q: e. Find points on the graph of xy°z² = 16 that are closest to the origin.

A: Let P be point (x0,y0,z0) Then, distance between P and origin is given by

Q: The population density of a city is given by P(x,y) = - 25x - 30y + 500x + 240y + 180, where x and y…

A: Population density is given by following function  P(x, y) = - 25x2 - 30y2 +500x + 240y + 180

Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: The function f(x,y) = 3x2 - 2xy + y2 + 8y has one stationary point. What is the location and…

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Q: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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Q: Determine the maximum r-values of r-7cos4e. 8- 0. * 3x 3x e= 0, e= 0, .

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Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x+2y=5.

A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

Q: Solve y′ = t − 5ty using both separable and linear methods, and verify that your answers are the…

A: Given data:   The given differential equation is: y’=t-5ty.     The given differential equation can…

Q: Find the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

Q: The position function of a particle is given by 7(t) = (t², 5t, t2 – 16t). When is th sneed a…

A: Given:

Q: What is the local maximum and minimum of the equation f(x)=x2e17x

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Q: Find least square quadratic approximation of function with f(-2) =0 f(-1) =5 f (0) =0 f (1) = – 5 f…

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Q: Suppose that a = 0.5 mi, vo = 9 mi/h, and vs = 3 mi/h as in Example 4, but that the velocity of the…

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Q: 2. Find an equation of the form f(x) =b.a +c that has the horizontal asymptotes at y = 350,…

A: y=b is said to be a horizontal asymptote of a curve y=f(x) if as x tends to infinity (or -…

Q: Suppose that f(æ, y) = e-2x² – 3y² + y Then the maximum is

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Q: Find a cubic function f(x) = ax + bx2 + cx + d that has a local maximum value of 4 at x = -3 and a…

A: Here we have to find the cubic function that has a local maximum value of 4 at x= -3 and a local…

Q: 11. The maximum point of the curve * y =r' - 3r° + 4 is at

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Q: Suppose that / (3r-x²) dr=Ax³+ Bx+C, for constants A, B, C. What is the value of C if the curve…

A: The given integral ∫3x4-x2dx=Ax5+Bx3+C

Q: Find the maximum value of f(x,y) = 14-x² - y² on the line x + 3y = 10.

A: Solution of given question is written in below steps.

Q: f(x) = 2x3+az? 12z has alocal maximum at z -2,then a

A: f(x)=2x3+ax2-12x  has a local maximum at x=-2then we have to find the value of a

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: The number of people P(t) (in thousands) infected t months after an epidemic begins 5 - where…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly aks…

Q: At what value of x does the curve y = x(x – a²)(x – b²) have a local maximum?

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Q: The quadratic function f is defined as f(x) = - (x+ 2)^2+ 3 Consider the graph of y = f(x) in the…

A: topic - graph of quadratic equations f(x) has vertex at (-2,3)  and y intercept at (0,-1)

Q: The function f(x, y) = -2x² + 4y² - 11 has a local minimum at the point (0, 0). Select one: True…

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Q: Q1. Determine whether this is a quadratic spline function T € (-00, 1] f(x) = {-(2 – x)² + T € [1,2]…

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Q: Find a cubic function y=ax³ + bx² +cx+d that has a local maximum value of 3 at -2 and a local…

A: According to our guideline the answer to answer only the first question if you want any particular…

Q: An electronics manufacturer determines that the profit P(in dollars) obtained  by producing and…

A: Consider the given function, Px,y=8x+10y-11000x2+xy+y2-10,000 Noe find the critical points by…

Q: Find the shortest distance from the origin to x2 − y2 = 1.

A: Definition used-         The shortest distance from a point to curve is the perpendicular distance…