Let (x, y) = 3y² - 2y – 3x² + 6xy. a. Find the equation of the tangent plane at the point (1, -1). b. Find all the critical points of f. c. Use the second derivative test to classify each critical point as a local maximum, local minimum, or saddle point.

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A: Use chain rule of partial derivative and simplify after substation.

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A: Given that: y2=x3a-x

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A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: Use the second derivative test to identify any critical points and determine whether each critical…

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A: A point (a,b) of function f(x,y) is said to be the saddle point if it is a critical point…

Q: (2) Let f(x, y) = x² – y². Find the tangent line to the level curve f(x, y) = -3 at (1,2).

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

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Q: (6) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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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)

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Q: Find the orthogonal trajectories of the one parameter family of curves ex+e-y=c

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Q: Find the orthogonal trajectories for the families of curves y+x^2 = w where w is a parameter

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Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

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Q: Find the orthogonal trajectories of the family of curves: y = k (csc x + cotx) Ⓒy²= 2 (C- cos x) O y…

A: This question is related to differential equations, we will solve it using given information.

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A: We will use matlab to find the answer

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Q: (4) Find the orthogonal trajectories of the family of curves z +y = 20C?, where C being %3D a…

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Q: Find using the appropriate Chain Rule for W =y- 7x*y where x = e° and y = e", and evaluate the…

A: The given function is w=y3-7x2y where x=es and y=et. Differentiate the function w=y3-7x2y partially…

Q: (c). If y = f(x1, x2, u, v), where x =h(u, v) фу and- pu Find total derivative Also draw their…

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Q: Find the maximum rate of change of f(x, y, z) = tan(2x + 7y + 3z) at the point (– 2, – 3, – 6). - -

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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: Let y=2x^2+7x+4. If Δx=0.3 at x=5, use a linear approximation to estimate Δy. Δy≈ ?

A: y=2x2+7x+4, ∆x=0.3 & x=5 Differentiating with respect to x, we get dydx=22x+71+0=4x+7 Now at…

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Q: Use the second derivative test to identify any critical points and determine whether each critical…

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Q: Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.) y = 19k

A: The objective of the question is find the orthogonal trajectories of the family of the curves.

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

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Q: (2) Find an equation for the tangent plane to the graph of z = where z = f(x, y) is implicitly…

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Q: Consider the function f(x,y) = -x³ + 4xy – 2y² + 1. Classify these critical points into local cal…

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C sin 0, where C being parameter.

A: See the detailed solution below.