(10) For the function S(1r, y) = 20* + ry² + 3a² + y², (a) find the critical points. (b) What information (if any) docs the second derivative test say about these critical points.

Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Introduction: If f(x,y) is a two-dimensional function with continuous partial derivatives and a…

Q: Find all local maximum and minimum points of y = 2 + 3x − x³ by the second derivative test.

A: y = 2 + 3x - x3    => y' = dy/dx = 3 - 3x2 = 0 (set)                => 3(1 - x2) = 0…

Q: 4. y = (8x*- 5x2 + 1)* 5. g(t) = -3V7t3 – 1

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Q: Let f (*= {(8) +f(9) for real values of x and y. If f '(0) exist 2 2 and equals –1 and f(0) = 1,…

A: Introduction :

Q: (b) A poll commissioned by a politician estimates thatt days after he makes a statement denegrating…

A: Given: Percentage of constituency that supports a politician is: St=75t2-3t+25t2+3t+25 Derivative of…

Q: Let f(x)=x+(1−x)^(1/2) Find the local maximum and minimum values of f using both the first and…

A: For local maxima or minima:The first derivative test is f'(x) = 0The second derivative test…

Q: Q-1Find the derivatives of the functions 1- Y+In (xy) =1 2. Inxf 9.

A: Note:- Derivative of the product of two functions is ddx fx·gx  =f'x·gx+fx·g'x   Part (1):-  Given…

Q: 6) Use derivatives to find where the function is concave up f(x)=x.e2x*

A: If  f "(x) > 0  on an interval, then f(x) is concave up on that interval.

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: 3) Let f(x)= 2x+3 . Calculate by definition f'(2).

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Q: 4)Given f(x) = 2x/(x2 + 1) a)Find the derivative. b)Find the critical numbers .

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Q: y" y' = Note: You can earn partial credit on this problem. Find the inflection points of f(x) = 6x4…

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Q: If f(z) = (3z -3)(2-22), use the product rule to find f'(0). %3D

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Q: Use the second derivative test to identify any critical point and determine what each critical point…

A: Critical point: The point where the function fx, y is defined and its gradient is a zero vector or…

Q: dx Vx -9

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Q: find all critical points of the function f x = x^−1 − x^−2

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Q: 1. Find the derivative of the following: a) 3x²+6x f(x)= 5x-1

A: according to bartleby guide line we do only first part of multiple questions…

Q: 6. Apply the First-Derivative Test, to identify all relative extrema of f(x) = x3- Answe homev 16…

A: Given query is to find the relative extrime.

Q: What is the value of the first order derivative of the closed function given as…

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Q: find derivative of y y= (3x²-3x+1)³/2 (3/2)(3x²-3x+1)¹/2 (6x-3) none of the above (3/2)(3x²-3x+1)¹/2…

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Q: derivative for this question. I gave the easy function. a) Domain of f(x) is b) Find the…

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Q: a) y = -5x6 b) y = 6x2 c) f(x) = -7

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Q: Find f. f "(x) = x-2, x > 0, f(1) = 0, f(7) = 0 f(x) =

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Q: Let f(x) be a function with second derivative of f"(x) = -(5x +11)?(x – 2) Determine the local…

A: When a function's at critical point x , and the second derivative at x is: less than 0, it is a…

Q: (ii) Show that {Xt} is stationary.

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Q: Find an equation of the tangent line to y = f(x) at x = -2. (Using the definition) f(x)=x² + x² + x…

A: we have, Differentiating w.r.t x, we getDifferentiating again w.r.t x, we getFurther,    .     .…