1. Find the domain of the following functions. f(x) = Vx2 – 9 + V16 – x2 a. b. f(x) = x2-25 1,

Q: Calculate the approximation for the given functionand interval:                    M4, f (x) =√x,…

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Q: Find the maximum and minimum value of f(x,y) =x3+3xy2-3x2-3y2+4

A: fx,y=x3+3xy2-3x2-3y2+4   fx=3x2+3y2-6x   fxx=6x-6   fxy=6y   fy=6xy-6y   fyy=6x-6

Q: s] B1(a): Find the value of k that makes function continuous at x = 4 x > 4 6x – k x < 4 3x + 6 f(x)…

A: The given function is fx=3x+6if x&gt;46x-kif x≤4. Assume that the above function is continuous at…

Q: Find and classify all the critical points of the following function: F(x,y)=(3x +4x')( y²+2y)

A: We need to find critical point and classify them.

Q: 2. Find and classify the critical points of the function f (x, y) = 6x2 – 2x³ + 3y? + 6xy

A: The solution is given below in the next step:

Q: d) Find the value of the constants ´ a ' and “ b ` that makes the function continuous at x=3 ; x3

A: f(x) is continuous at x = k if

Q: 4. For the below function, find the stationary point (s) and prove if a maximum, minimum, or saddle…

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Q: find all possible functions with the givenderivative. y' = 1 - 1/x2

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Q: Determine all the critical points for the function. f(x)=6x^5+33x^4−30x^3+100

A: We have to determine all the critical points for the function  f(x) = 6x5 + 33x4 - 30x3 + 100 We…

Q: Find the value of constant K that makes the function below continuous at x = 2. -2x X < 2 X-2 f(x)…

A: Given,           fx=x2-2xx-2 ; x&lt;2kx-3 ; x≥2

Q: If the critical point of the function f(x.y)-x- y- 2xy +6 is (0.0). test this point whether it is:

A: We use second order partial derivative to know about critical point behaviour

Q: Are the f-llowing functions Continual s OFC メーE X-2 スト=メ 1P 2) FCX)s X- S X +7 at XE-1 X5qXs (xフゴ

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Q: Find the absolute maximum and absolute minimum of the function f(z) = z² – 6z + 5 over (1,

A: Given: fx=x2-6x+5, 1,6

Q: (1) Where on the line r = ay does the function f(x, y) = (x – a)² + (y – 2)2 attain its smallest…

A: The line whose equation is of the form y=mx is passes through the origin and slope of the line is m.

Q: Find and classify the critical points of the function f (x, y) = 16x³ – 12x2 + 12xy? + 3y?

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Q: Find the local and absolute extremum for the functions over their domain: 5. f(x) = vx2 + 8x + 20

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Q: Find all critical points of the function:  f (t) = 8t3 − t2

A: If f has a local extremum (maximum or minimum) at C and if f'(c) exists, then f'(c)=0. A critical…

Q: Find the maximum and minimum values of the function f(x) = x² – 6.x +7 on the interval [0, 5].

A: It is given that, f(x)=x2-6x+7   , on the interval 0,5We have to find the maximum and minimum values…

Q: Find the critical points of the following function. f(x) = 5x? + 3x +2

A: Given,          The function is fx=5x2+3x+2.

Q: Find the linear approximation of the function at the given point. ffx y)=-9x2-6y2+ 6 at (6,-10)…

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Q: Find the Quadratic approximation of the function at the given value f(x) = 1n(x + 1)     near a = 0

A: Given  The function is f(x) = ln(x + 1)     near a = 0 .   Formula for Quadratic approximation :-…

Q: 1. Come up with the equation of any function f (x, y) satisfying fx = x + y and fy = x + 3y³

A: The objective is to find the function f(x,y) satisfying fx=x+y and fy=x+3y3 Now take, fx=x+y Now…

Q: Find the maximum and minimum values of f(x, y)=x+3xy2-3x2-3y²+4.

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Q: Consider the function f(x) = - 2x + 24x2 42x +4. %3D - Find the critical points.

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Q: Find the critical point of the function f(x, y) = – 7 2x + 5x2 - 8y – 5y? |

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Q: Use the second derivative to determine f"(4) for the function f (æ) = x² In (x) 2ln(4) +2 3ln(4) +3…

A: Derivative of the function

Q: 9. Let f(x) = x³ – 3x² + 3. a. Find the y-intercept of the function; b. Find all critical points of…

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Q: Consider the function f(x,y) - x-44x- 4y and determine if, at the point (4,0) if the function is a…

A: Note: Since you asked multiple questions I solved one. For solution of other problem please post the…

Q: Find the values of a and b so that f will be differentiable at x = 3.

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Q: Find the global extrema of the function f(x)=e−x2.

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Q: Find the maximum and minimum values of the function f(x,y)=2x^2+3y^2−4x−5 on the domain x^2+y^2≤9.

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Q: Find the streamlines corresponding to: f(z) = z²

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Q: Find the maximum and minimum values of the function f(x, y)-xy subject to g(x, y) = x² + xy + y² =…

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Q: Consider the function f(x, y) = e-xy It is possible to state that f reaches global extremes (global…

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Q: Find the linearization of the function f(x) = 1/(9x+8) at x = -1.

A: Topic : function

Q: 8. (a) For f(x) = Vx, give the linearization at a = 25. (b) Use your answer from part a to approxi-…

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Q: 1 Find the length of the curve f(x) + from x = 2 to x = 4. %3D 6. 2x

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Q: find the critical point and classify the function f(x,y) =xlny +x2 -4x-5y+8

A: Answer

Q: Find the lineearization L(x) of the function f(x) = x^3/4 at x = 16.

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Q: Find minimum and maximum for the function 6 x + 4 y under conditions: x2 0; yz 0; -x+y s 12; x+ys…

A: The objective is to find maximum and minimum value of the function 6x+4y.

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: Find the critical point of the function f(x,y) = 7x²y² + 4y² + 4x².

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Q: determine all critical points for the function: y = x^3 + 9x^2 - 48x + 10

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Q: Find the local extrema of the function f(x)=√x2+1.

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Q: The equation of the tangent line for the function f(x) = -8 – 5x at a = 8 is %3D y = -5(x + 8) + 48…

A: Given that      f(x) = -8 -5x at x = 8 We have to find the equation of the tangent line for the…

Q: 4. Determine the minimum value of the function y = f(x) defined implicitly in the equation x² + 3xy…

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Q: Locate and classify all the critical points of the function.(If an answer does not exist, enter…

A: We need to classify all the critical points of the given function.

Q: Find a good numerical approximation to F(4) for the function with the properties that F'(x) = e-x+15…

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Q: Use the second derivative to determine f"(3) for the function f(x) = x² In (x) 2ln(3) +2 O 3ln(2) +3…

A: topic - derivatives

Q: Show that a function f decreases most rapidly at x in the direction opposite to the gradier (that…

A: Solve with given conditions