Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

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: Determine the values of x where a curve y = x3 - 3x2 - 9x+ 12 has horizontal angent lines.

A: Given,         y=x3-3x2-9x+12

Q: find the orthogonal trajectories of the family of curves x2+y2=a2

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Q: Find a point c satisfying thr MVT for the given function and interval  y=x/x+2 [1,4]

A: Given query is to find the value of c.

Q: Find the maximum rate of change of the function f(x, y) : 4y4 at the point (1,3)

A: We will solve the problem

Q: i) Find the orthogonal trajectories of the family of curves: y : 1+ x?

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems

Q: Find the linear approximation of the function at the given point. f(x y) = 4x²y3 at (-9,7) O A. L(x,…

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Q: Find the shortest distance between the line y - x=1 and the curvex =y.

A: NOTE: Refresh your page if you can't see any equations. . the given line is  compare this…

Q: The slope of the curve f(x)= at x =1 is

A: given function :

Q: What is the equation of the line normal to f(x) = 5x5 – 2x at x = -1 %3D

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Q: Determine the coefficients a, b, c and d so that the curve y = ax³ + bx² + cx + d be tangent to the…

A: Curve y=ax3+bx2+cx+d is tangent to the line y=3x+8 at the point (-2,3). The curve y=ax3+bx2+cx+d has…

Q: Show that the curve y =(1 + x)/(1 + x2) has threepoints of inflection and they all lie on one…

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Q: When we are standing at the point (1,-3), the function f(x, y) = 3x²y+xy is increasing most rapidly…

A: We have to find the direction of  rapid increase of the function using gradient of the function.

Q: Find the orthogonal trajectories for the family of curves y=c1x4

A: First of all rearrange the given equation in such a way that both the variables be on one side of…

Q: Make the curve y= ax2+bx+c pass through (2,1) and be tangent to the lane y= 2x +4 at (1,6)

A: The given curve passes through (2,1) ⇒1=4a+2b+c                                    (1) And the curve…

Q: Find the line tangent to the curve x + yi = 4 at the point (3V3, –1). y = x- 4 Oy = x+4 y = O y= s…

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Q: Determine slope of a curve y = x³ + 1 at x = 1

A: Given,           The slope of the curve y=x3+1  at x=1.

Q: Find the absolute maximum and minimum of the function on the given domain. f(x.y) = 6x + 5y on the…

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Q: Find the orthogonal trajectories of family of curves x-y=cx^2

A: To determine the orthogonal trajectory of the equation f(x,y)=c Find dydx Replace dydx→-dxdy Solve…

Q: Find the orthogonal trajectories of the family of 1 curves Y= X + k

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Q: Find an equation of the parabola y = ax2 + bx + c that passes through (0,1) and is tangent to the…

A: Since, the parabola passes through (0,1) ,so,we substitute x=0, y=1 ,to get c=1

Q: The student should determine the minimum rate of change of the function g(x, y) = y²e*Y on the…

A: First I have written the rule of minimum rate of change of a function at given point and then find…

Q: Determine slope of a curve y = x³3 + 1 at x = 1

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Q: 3) Calculate the length of the curve interval [-2₁2]. y = x²/2 on the

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Q: Find the orthogonal trajectories for the family of curves. (Enter your solution in the form F(x, y)…

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Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: Find the slope of the curve x^2 + y^2 - 6x + 10y + 5 = 0 at point (1,0) * O 1/5 O 2/5 O 1/4 2 O O O…

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Q: find the length of the curve 3y2=4x3 from x=0 to x=8 when y greater than or equal to 0.

A: The formula for length of a curve f(x) extending from point a to point b is given as,

Q: Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

A: x=13yy-3,   1≤y≤9 Differentiating with respect to y, we get…

Q: B. Find the length of the curve y = x² from x 0 tox = 4.

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Q: Make the curve y=ax²+bx+ c pass through (2,1) and be tangent to the line y=2x+4 at (1,6)

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Q: Determine the critical points of the curve y = x³ – 5x2 - 36 x + 25.

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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: The line that is normal to the curve x2 + 2xy - 3y2 = 0 at (1, 1) intersects the curve at what other…

A: Given thatx2 + 2xy – 3y2 = 0          …(1)On differentiating equation (1) with respect to x,

Q: Find the gradient of the curve y = a²xe-b*x at x = 1.

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Q: The slope of the secant line of the function y =Vx +x through the points x, = 1 and the point xz = 4…

A: y=x+x

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

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Q: Find the linear approximation of the function y = x' at point xo 1 О а. у %3D Зх — 2 -

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Q: Draw the level curves for the function z = f(x, y) given by z = /4 – x² – y² when z = 0, 1, 2 and…

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Q: Find the orthogonal trajectories of the family of curves x2+y2=a2

A: We have to find the orthogonal trajectories of the family of curves x2+y2=a2.

Q: Find the orthogonal trajectories of the family of curves x3y-xy3=c where c is constant

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Q: Find the point where the minimum value of f(x, y) = xy subject to y = 90 – x occurs.

A: Find the point where the function f(x,y)=xy subject to y=90-x2 attains its minimum value.

Q: Find the maximum slope on the graph of f(x, y) = 2 sin(ry) at the point P(4, 0).

A: The given question can be solved as shown in step2.

Q: Show that the function f(x, y) = 3x - 4y² is differentiable at point (−1, 2)

A: answer is in next step. please give a like !!!

Q: Find the maximum rate of change of the function f(x, y) 4y5 at the point (5,4)

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Q: Find the equation s for the perpendicular trajectories of the curve family. 1. x -

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Q: Find the direction at which the function f (x, у, 2) %3 хIn(е' — хг) increases fastest at (-3,0,0)

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Q: Find an equation of the line tangent to the curve y = v4x – 3 – 1 and perpendicular to the line x +…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.