The curve y = 2x² +- k has a gradient of 5 when x 2. Calculate: (а) The value of k. (b) The minimum value of y.

Q: Find the gradient of the function f(x,y) = 4y - 9x at the point (9,3). Then sketch the gradient and…

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Q: Find the points on the curve y=x(x-1)(x-2) which have the same gradient use @ for 2

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Q: The line 3x + 2y +14 0 has a gradient of and y-intercept of Where appropriate, give your answer as a…

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Q: 5. Find the gradient of the curve i) y = 3e-2x – 1 at the point where x =. ii) y = xv2x - 3 at the…

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Q: ,2 For function f (x, y) x2+1 Evaluate the gradient at the point (1,2)

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Q: a. What is the gradient at the point (4,0,1)?

A: Consider the given function fx,y,z=x2+y2+2z2+3.  The gradient of a function is given by,…

Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: f(x,y)=x² +16xy + y² +8

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Q: Find the gradient of the function g(x,y) = xy at the point (3, - 1). Then sketch the gradient…

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Q: Find the gradient of the function f(x.y) = /2x+ 3y at the point (- 1,2). Then sketch the gradient…

A: Solve the following

Q: How do you compute the gradient of the functions ƒ(x, y) and ƒ(x, y, z)?

A: Given, The function f(x,y). It's gradient is given by, For example,

Q: Which of the following is the gradient vector of the function f(x, y) = 3x ln 3y - 2x²y at point (1,…

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Q: Find the coordinates of the points where the gradient is zero on the curve y = x + . Establish…

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Q: The gradient of f(x,y,z)=xy2z3f(x,y,z)=xy2z3 at the point (1, 1, 1) is

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Q: Find the gradient of the function and the maximum value of the directional derivative at the…

A: Gradient of a function f(x,y,z) is given by,          grad(f(x,y,z))=i∂∂x+j∂∂y+k∂∂zf(x,y,z)…

Q: Q3. Find the coordinates of the point(s) of the function y=3x – 5x +2, where the tangent has a…

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Q: c. y = 2Vx when x = -1 с.

A: We have to find the gradient

Q: Find the gradient of a normal line to the parabola y=x^2+5x-9 at the point (1,1)

A: In this question, the concept of slope is applied. Slope A line's slope or gradient is a number that…

Q: Find the gradient of the ellipse 2x2 + 3y2 = 14 at the points where x = 1

A: It is given that the equation of an ellipse is ;  2x2+3y2 = 14 We have to find the gradient of the…

Q: Find the gradient of the function at the given point. y Ri (2, 2) x²+ y2' Vf(2, 2) = %3D Find the…

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Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² I in the…

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Q: Find the gradient of the function at the given point. Function Point (7,4) f(x, y) = Vf(7, 4) = x +…

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Q: b. y = 2x2 when x = 6 %3D 3.

A: Consider the curve: yx=2x23 at x=6. Find the gradient of the curve at x=6.

Q: What is the gradient of f=x^2+y^2-2xy-x+3y-z=-4 ?

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Q: The gradient of f(x, y) = xy at (x, y) = (2, 3) is

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Q: Find the minimum rate of change at (2,-2,0) and it's direction for f(x, y, z)= =. zy² H in the…

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Q: The table shows experimental valucs of two variables x and y. 0.1 0.5 1 1.5 2 y -5.95 1.63 0.83 0.61…

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Q: Find the coordinates of the point(s) at which the curve y = x-2/3 has gradient – 1/6. %3D -

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Q: There is a tank in the shape of a paraboloid:   Water is being pumped into the tank at a constant…

A: Water is being pumped into the tank at a constant rate of 2π cubic inches per minute. If y denotes…

Q: Find the gradient of the function y = x³ + x² – 2x at points where - a. It crosses the x -axis b. It…

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Q: Find the gradient of ?:V x²+y²1Z²

A: Gradient of a function f(x,y,z) is given by ∂f∂xi  ∂f∂yj + ∂f∂zk

Q: Find the gradient of pthe function and the maximum value of the directional derivative at the point…

A: To finds the gradient of the funxction and the maximum value of thedirectioonal derivative at the…

Q: Find the gradient of the function at the given point. In(x - y)- 4, (3, 8) Z = Vz(3, 8) =

A: The objective is to find the gradient function at the given point.

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: The probability of not matching the salt content of sand from a particular source is 0.2, and the…

A: GivenThe probability of not matching the salt content of sand from a particular source =0.2 The…

Q: Find the gradient of the function at the given point. Function Point x + 2y y + 1 f(x, у) 3D (1, 2)…

A: Find the gradient of the function at the given point & find the maximum value of the directional…

Q: What is the gradient of f(x, y, z) = x³z2 + y³z +125z - 1 at P(5,5,-1) ?

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Q: First, compute the gradient of the function p(x,y)= 12- 2x-y Then evaluate it at the point (- 1,2).

A: We need to find partial derivatives with respect to x and y to find gradient

Q: Determine the gradient of the curve 3xy + y² = -2 at the point (1, -2)

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Q: Find the gradient of f(x, y) = 3xty3 + 4x°y® at (1, 2).

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Q: Find the gradient of the function f(x, y) = 7x2 + 6y, at the point (-2, 6). [ i.e., find V f(-2,6) ]

A: As we know that the expression of the gradient of the function is: ∇fx,y=i∂∂x+j∂∂yfx,y Given:…

Q: Find the gradient of the function at the given point. In(x2 – y) - 3, (3, 8) Z = | Vz(3, 8) =

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Q: Find the gradient of the function g(x, y) = 2xey/x , at the given point (2, 0)

A: Consider the given: gx,y=2xeyx,2,0Gradient of the function…

Q: Find the gradient of the function at the given point. In(x² - y) - 9, (2, 3) = Z Vz(2, 3) =

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Q: If ø = 3r²y – y³,2. Find gradient Vø at the point (1, –2, –1).

A: The solution is given as

Q: Find the gradient for the curve defined by y + xy = 3 at the point (1,2)

A: Gradient to given curve

Q: Vhat is the gradient of g(x.y) = ye* and its maximum value of its directional derivative at P(0, 5)?…

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Q: Find the gradient of the function at the given point. Function Point (8,4) f(x, y) Vf(8, 4) = = = x…

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Q: Find the gradient of the function w = 6xy − y2 + 2xyz3, at the given point  (−1,  5, −1)

A: To find the gradient, take the derivative of the function with respect to x,y,z.