Where does the relative maximum value of f occur when f' (x) = x³ – x ? (а). —1 (b). О (c). 1 (d). 2

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Q: 9) Where is the function ht) = (t+ 5) differentiable?

A: Given         h(t)= t+51/3

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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

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A: To Determine: find the maximum rate of change of the following function at the given point . Given:…

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A: To determine two functions having the prescribed Wronskian and decide on their linear independence

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A: Given u(x) = 2x-12 + 3-4x14 + 2

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Q: Find the derivative. (Hint: en a = x) %3D y =S 4 In x et dt O * - 1 4x3

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Q: Find the lineari zation L (x) of the fuction at a. f) = x'+2x

A: In the given question we have to find linearization of function.

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A: We have to find which variable should we choose so that we differentiate as quickely as possible.

Q: 8) Find the linearization of f(x) = 6 + X+1 tan 4 dt at x = 0. 1.

A: On solving this we will get

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A: Second derivative is positive.

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Q: 4. Find the differentiation dy. using definition with limit of the following: y = V2x + 1.

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Q: Show that f(x,y) = 1-x* - y* has a relative maximum, even though D in the theorem is 0. The critical…

A: Given : f(x, y) = 1 - x⁴ - y⁴

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Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: 2. Show that the function psin(2r) e-*dt g(x) = is differentiable on R and compute its derivative.

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Q: 4. Show in two ways that the function f(z) = exp(z²2) is entire. What is its derivative? Ans. f'(z)…

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Q: Approximate the critical points of g(x) = x cos−1 x and estimate the maximum value of g.

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Q: 2. Find the orthogonal trajectories of the family of curves x2 + y² = 2my where m is a constant.

A: As given equation of curve is: x2+y2=2my Differentiate it with respect to x:…

Q: 2. Find the critical points of f(x, y) = x³ + 2y³ – xy and analyze them using the Second Derivative…

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Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

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Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

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Q: Suppose that the function f(x, y) = x°y+ax – 8y + 5 has a critical point at (2, –2). What must the…

A: For a function of two variables, f(x, y), a critical point is defined to be a point at which both of…

Q: Consider the Cobb-Douglas production function f(x, y) = 100x1/3y2/3 where x is the number of units…

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Q: 4x 28. If R = and errors in x, y, z be 0-001. Show that the maximum relative error at x = y = z = 1…

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Q: Find the point at which the function f(r,y) = 2 in z+2 In y attains a maximum subject to the con-…

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Q: Let y = 5x² + 4x + 4. If Ax = 0.3 at x = 4, use linear approximation to estimate Ay Ay ~ Submit…

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