Find all points (x, y) where the functions f(x), g(x), h(x) have the same value: 8 f (x) = 2"-5 + 3, g(x) = 2x – 5, h(x) = + 10

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: Find an equation of the secant line containing (1, f(1)) and (2, f(2)). f(x) = x² - 2x %3D

A: Given , the function f(x) = x2 - 2x Now we find      f(1) = 12 - 2•1 = 1 - 2 = -1,…

Q: - f(x, y) = Vx5 + y5. Find f-(0, 0).

A: Given that fx,y=x5+y55.It is required to find fx0,0.

Q: Find the linearization of-ƒ(x, y) = x2 - xy + 1- 2 y2 + 3?

A: Here we have,  f(x,y) = x2-xy+1-12y2+3 at (3,2)

Q: The function y=f(x) satisfies the conditions y(0) = 1 and y'=xy³/4. What is y(1)?

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Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7. fxy(x,y)=

A: Concept: Partial derivatives: In differential geometry and vector calculus, the partial derivative…

Q: The graph of the linear function f(x) passes through the point (x, y) = (1, m), where m is the slope…

A: Given:Graph of f(x) passes through the point (x, y) = (1, m), where m is the slope of the line.

Q: Find the local extreme values of the function ƒ(x, y) = xy - x2 - y2 - 2x - 2y + 4.

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Q: Find the local extreme values of ƒ(x, y) = x2y on the line x + y = 3.

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Q: The function f(x, y) = -3y + 2√√ry is a

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Q: Solve for the domain and range of. f(x,y,z) = %3D V4-x2-y²

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Q: find the general equation of : x^3dy+xydx=x^2dy+2ydx  ;y=e when x=2

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Q: Differentiate the function. y = (3x- 2)² (1 –x³)² dy

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Q: Find domain and range F(x,y)= Vx-1

A: Since you have asked multiple questions in a single request, as per policy, only the first question…

Q: Maximise the function f(x, y) = 4xy² subject to r + y? = 2.

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Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: In this question given that two line which are intersect each other and and a line is perpendicular…

Q: Find the indicated value of the function f(x,y,z)=2x-7y + 4z³ -7. f(6, -5,3) f(6, -5,3)=

A:

Q: Find fxy when f(x, y) = 8xeXy.

A: To find fxy when fx, y=8xexy.

Q: Find fxy(x,y) if f(x,y) = (x5+y³) 7. fxy(x,y) =

A:

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

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Q: For the function f(x,y,z) = 3 + xy5 - 5z4, find fx , fy , and fz.

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Q: Find the values of ôf / ôx at the point (4,-5) if f(x, y) = x +3xy + y-1

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Q: Find the relative maximum and minimum values. Зx2 f(x,y) = + 10y2 + 3

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Q: Find the point at which the line f(x) = - x – 2 intersects the line g(x) 3x + 6 %3D

A: f(x) = g(x) Thus, -x-2 = 3x + 6   Separate variables to LHS and constants to RHS -x-3x = 6 + 2 -4x =…

Q: Find f, (x.y) if f(x.y)=x - 5xy- 4y2.

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Q: How can you display the values of a function ƒ(x, y) of two in-dependent variables graphically? How…

A: For a  function ƒ(x, y) of two in-dependent variables. It can be plotted graphed using 3d plotting…

Q: The derivative of the function y = 7x² + 12 – is: - 15 a) y' = 14x + x2 15 %3D b) y' = 14x + %3D c)…

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Q: Find the area of a triangle bounded by the y axis, the line f(x)=8−13x, and the line perpendicular…

A: Recall : Area of the triangle with three points x1,y1,x2,y2 and x3,y3 :            A=…

Q: Find (x, y): R = {(x, y): 0 ≤ y ≤ √√x² +1,0 ≤ x ≤ 1} about the x-axis.

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Q: xyz 9. f(x, y, z) = x² + y2 + z2

A: Givenf(x,y,z)=xyzx2+y2+z2To find Domain of above functions

Q: The demand and supply functions for a certain brand of breath mints are demand =−20x + 150 and…

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Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: The product of slope of perpendicular lines is -1  and slopes of two parallel line are equal. The…

Q: How do you linearize a function ƒ(x, y) of two independent variables at a point (x0, y0)? Why might…

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Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: Solve for fazy for f(x, y, z) = 4x³y²z - e²zy¹ + + 4y - x¹6

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Q: Find f, for the function f (x, y) = yx-2z'y %3D

A: we have to partially derivative

Q: 11. Perpendicular to 5y = 2x – 6 and passes through the point (-1, 5)

A: topic - equation of a line perpendicular to given line

Q: Find all the stationary points of the function f(x,y) = x3e-(x^2+y^2).

A: Given:

Q: В. Find az if z = f(x, y) is implicitly defined as a function of x and y for the equation below…

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Q: Calculate fxyy for f(x,y) = x 3 + y2ex.

A: Given function is fx,y=x3+y2ex. To calculate: fxyy. Solution: fxyy means first partial derivative of…

Q: For the function f (x) =x³ – 3 -x² + 8 , find the coordinates of all Critical Points.

A: Given, fx=x3-3x2+8

Q: Find the equation of line (L) that passes through the intersection point of the two functions y = v2…

A: Given functions: y=2-x2y-2x+3=0 Equation of perpendicular line is, 2x-4y=6

Q: Suppose that f(x, y) = 32 y at which {(x, y) | æ² + y² < 3²}.

A:

Q: Differentiate with respect to t 100 = x2 + y2

A: give equation ;- 100=X2+Y2 when we differentiate above equation with respect to t , we get

Q: Find fxy(x,y) if f(x,y) = (x5 +y³) 7.

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Q: The population density of a city is given by P(x,y) = - 20x - 20y + 560x + 440y + 200, where x and y…

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Q: Find DF of fcx,y)=x²e° at the point (-2,0)-

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Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.

Q: Solve for the domain and range of. f(x,y,z) = V4-x2-y?

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.