(g) f (x,y,z) = x² + y? – 2z? + zlnx in P(1,1,1) (h) f(x,y, z) = e*+Ycosz + (y + 1) sin -1x in P(0,0,/6)

Q: What is the gradient of the function f(x) = -x² %3D A -x? E -2x C 2x H -1 1

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Q: uppose the temperature of coffee changes with time as shown in the following table Time (minutes…

A: Step-By-Step solution of the question is given below.... Suppose the temperature of coffee changes…

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: f (x) = x2 – 2x + 2 | P 3 3+h an expression for the gradient of the line joining the points, P and…

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Q: Find the local maximum, minimum and saddle points of the function using the second derivative test:…

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Q: Determine for the following equations whether y is a function of x. Justy your anwer. -x2+y4=4

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Q: Define gradient.

A: To defineGradient

Q: 8 f(x, y) = y/x, P(1,2), u = }(2i + 5 j) |(2i + /5 j)

A: To find the gradient at the given point and then rate of change for the given function.

Q: Find the gradient of the following function. 3 f(x, у) %3 5x° - ху Vf(x, y) =

A: Gradient of f(x,y) is given by∇f(x , y) = i⇀ ( fx ) + j⇀( fy )

Q: Find the Re

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Q: Find the maximum rate of change of f at the given point and the direction in which it occurs. f(x,…

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Q: Find the gradient of f(m, n) = m³ +n³. grad f = i +

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Q: Determine the position function, s(t),

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Q: 4. y = V6 – 7x

A: Definition used -                         Power rule of derivative -…

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 function for: 21y-

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Q: Find all functions from X = {a,b} to Y = {p,r,t}.

A: Given :- To find all functions from X = a,b to Y= p,r,t.

Q: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1