You are at position (2, 1). For each function in Q1, (a) What is the steepest direction? i.e. write down the normalized gradient vf(2,1)|| | Vf(2,1) (b) Find the directions (unit direction vectors) u that cause you to "walk along the side of the mountain without going up or down." That is, find u that solves u. Vf(2,1) = 0, subject to ||u|| = 1. %3D

Q: The line with equation 7x + 5y – 4 = 0 (a) Cuts the x-axis at the value x = (a) Cuts the y-axis at…

A: The equation of the line is: 7x+5y-4=0 The problem can be solved as follows:

Q: 4. If A is the point with coordinates (1, 4). B is the point with coordinates (7, 22). Find the…

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (1, 5) Vf(1, 5) =

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 2y2 + 4, (4, 2) Vf(4, 2) =

A: Topic = Functions

Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 4, (1, 2) Vf(1, 2) =

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 5y² +6, (3, 1) Vf(3, 1) =

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

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Q: Find the gradient of the function at the given point. f(x, y) = 3x + 5y2 + 8, (2, 1) Vf(2, 1) =

A: We have given function  fx,y=3x+5y2+8 fx=∂fx,y∂x fx=3∂x∂x+5∂y2∂x+∂8∂x fx=3+0+0 fx=3  .........(i)…

Q: Find the gradient of the function w = 2x²y - 4yz + z² at the point (1, 1, -2). ○ 2î+ 10j - sk Ⓒ41+…

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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: Q3: Find gradient of the following function at given point f(x, y. =) = (x² + y° + :')"? + In(xyz).…

A: The detailed solution is as follows below:

Q: Q3: Find gradient of the following function at given point 3) f(x, y, 2) = x² +y² – 2=² + = In(x).…

A: The gradient at the point (1,1,1) is, (3, 2, - 4)  The detailed solution is as follows below:

Q: First, compute the gradient of the function p(x,y) = /13- 2x - 3y. Then evaluate it at the point (-…

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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: 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 function at the given point. In(x? - y) - 3, (2, 3) Vz(2, 3) -

A: We have to find the gradient of the function z = lnx2-yx-3 at the point 2, 3.

Q: The gradient vector of the function f(x, y) = cos(4x - 6y) is (4 sin(4x - 6y), -6 sin(4x - 6y)).…

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y2 + 6, Vf(4, 2) = eBook

A: A detailed solution is given below

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: at the point (In 12,2) Find the gradient for the function f(a, y) = y'xe # Find exact values. No…

A: The given function whose gradient is to be calculated at a given point is:

Q: Given the function z = f(x, y) = 3x² +6xy + y² + 8y, find the following: a) Find gradient at (-2, 3)…

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Q: Find the gradient of the function at the given point. f(x, y) = 2x + 4y2 + 1, (1, 5) Vf(1, 5) =

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Q: Find the gradient of the function w = 2x²y – 4yz + a at the point (1, 1, -2). O 2i+ 10j- 8k O 4i+…

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Q: Calculate the gradient. h(x, у, 2) %3 хуz7 Vf =

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Q: A line I has a gradient of m₁ = Which one of the following lines will intersect I at right angles? 4…

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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 function for: 21y-

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Q: Find the directions in which ƒ(x, y) = (x2/2) + (y2/2) (a) increases most rapidly at the point (1,…

A: We have to find the directions a) Given function is  f(x, y)=x22+y22∆f=∂f∂xi^+∂f∂yj^∆f=122x i^+122y…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y² + 8, (2, 1) Vf(2, 1) =

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Q: Find the gradient of the function at the given point. g(x, y) = 5xev/x, (8, 0)

A: Follow the procedure given below.

Q: 1. Find the Gradient of the following a. F, = x'e" - y': b. F, = 4x' - 3y +5=?

A: Solution is given as below:

Q: Find the gradient of the function at the given point. w = 5x²y-7yz+z², (1, 1, -2) O 15i+ 26j+ 11k O…

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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: w = 3x² – 5y² + 2z², (1,1, –2)

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Q: Find the gradient of w= 3x² - 5y* + 2z at the point (1, 1, -2)

A: The given function is: w=3x2-5y2+2z2

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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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: 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

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: Find the gradient of the curve . Y=4x^2 at x=3

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Q: Q3: Find gradient of the following function at given point 1) f(x,y)=y-x, (2,1)

A: We find the gradient of the given function by using the definition of gradient. The gradient of a…

Q: First, compute the gradient of the function f(x.y) = 3+ 3x - 7y. Then evaluate it at the point (-3,-…

A: Given:      f( x , y ) = 3 + 3x2 - 7y2      Point : ( -3 , -4)

Q: First, compute the gradient of the function p(x.y) = /33 - 3x - 4y² . Then evaluate it at the point…

A: Solution: The objective is to find gradient of the given function

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

A: The solution is given as

Q: For curve with equation f(x) =x²(x² – 1) find a. The coordinates where its gradient is zero b. The…

A: The gradient of a function f(x) is given by its derivative w. r. t to 'x' that is f'(x).  The…

Q: Find the gradient of the function at the given point. f(x, y) = 4x + 2y² + 4, (1, 2) Vf(1, 2) =

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Q: Find the gradient of the function at the given point. f(x, y) = 4x + 3y2 + 1, (1, 4) Vf(1, 4) =

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