Consider the function y = (x) where f(x) = x³ +2x2 - 4x and g(x) = x2 + 2. Determine a) the domain and b) the end behaviour of y = ) (2).

Q: Determine the domain of the function f (x, y) In(3-y) 4- x2 – y2°

A: Given function is f(x,y)=ln(3-y)4-x2-y2 Domain is the set of values for which the function is real…

Q: For what value of x does the function f(x) =x³ – - 4x attain the absolute maximum in the interval…

A: Second derivative test: If the function f is twice-differentiable at a critical point x (i.e. a…

Q: 1. How to define the function, f(x, y) = 15x+4x*y+15y 3x+3y to make it a continues function?

A: We have to find the given function is continuous.

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Q: Find the inflection point of the curve f(x)= x³ – 12x²+7x+1.

A: An inflection point is a point on the graph at which the second derivative is equal to zero or…

Q: The domain D, of the function f (x) = Vx² – 1 is: -

A: The domain of a function is set of values for which the function is defined. The square root is…

Q: Differentiate f(x) = a4x4 -3ax² with respect to x. Assume that a is a constant. f'(x) =

A: f(x)=ax4-3ax2 differentiate with respect to x

Q: Find the points of discontinuity of the function f(x)={1−x2,x<0x+2,x≥0 if they exist.

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Q: ax+bx+4 ifgと- ニ bx*-2 × ifメ

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Q: Suppose that f(æ, y) = e-3x² – 4y? + y Then the maximum is

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Q: Find the point at which the line f(x) = - 3x 3 intersects the line g(x) = - 2x

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Q: f f(x,y)= √(2x2 + 2y2 - 8)

A: As the function is defined in terms of square root, the function is well defined only if the…

Q: Let f(x) = x^2 −x −2. Using the Intermediate Value Theorem, explain why this function has (at least)…

A: The function is  f(x)=x2-x-2

Q: Find the absolute maximum value of y=sqrt(16-x2) on the interval [-6,6]

A: y=16-x2         -6,6y=16-x212ddxy=1216-x212-1.0-2xdydx=12-2x16-x212dydx=-xx116-x2Now , dydx=0…

Q: Differentiate the function f(x) = In(6x7 – 4x) + v2 – e3x. - -

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Q: urve: f(x) = x4 − 6x2

A: Given,          f(x)=x4-6x2

Q: Find the linearization of the function at a . f(x) =  x3/4    , a = 16

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Q: The function f(x,y)=/26-2x²-y² is continuous at point (2,-3). .A False .B True

A: A function is continuous at a point if after putting the point in the function yields a positive…

Q: Let f (x) = 2x and g (x) = 3x2 + 1, find(go f) (x). Show your work using the Equation Editor Tool.

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Q: Find the co-ordinates of the minimum turning point for the function f(x)= 2x² + ± 4 Using the second…

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Q: Show that f(x) = 3x². x is not differentiable %3D

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Q: What is the domain of the function y = x+ V9-x²

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Find the interval on whih f(x) =x2-3x+8 increasing or decreasing

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Q: Coo show that the f(x,y)=X+4xy-3y gdegrad is homogenaow of

A: Concept used: The function is homogeneous of degree n if fkx,ky=knfx,y. Given: fx,y=x3+xy2-3y3…

Q: Linearize the function f(x) = x3 + 2x + 4 at a = 3.

A: To linearize a function  at certain point x=a , first we need to evaluate the function value at a (…

Q: Consider the function F(x)= (x+2)^2 for the domain [-2, ∞)

A: Given           Function is :                            F(x)=(x+2)2 for the domain [-2, ∞)   To…

Q: Given the funci f(x + 1) = f(x) + f( – 3) = %3D - ||

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Q: Find and sketch the domain of the function. f(x, y) - In(4x2 - 4y²) y

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Q: A once-popular dog’s chew toy is slowly declining in popularity. The quartic function…

A: Given that x is the number of years since 1993 So 2001 means x=2001-1993=8

Q: A once-popular children's doll is slowly declining in popularity. The quartic function f(x) = -…

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Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…

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Q: 5. Use the second derivative test to determine whether f(x) has local maximum or local minimum at…

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Q: Find an sketch the domain of f(x,y)= 16x² – x² –4y². -

A: Given that fx,y=16x2-x2-4y2 To determine the domain of the function. fx,y is only defined for…

Q: differentiate find f'(t) for f(x)=(2x-2)(3x^3-x^2+1)

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Q: Find the point at which the line f(x)=−x−4 intersects the line g(x)=5x+14.

A: On solving this we will get

Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests.…

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Q: Find the greatest and the least values of the function y = x³ – 3x +3 on the 2 (a). interval [-, ).

A: Solve the following

Q: Let f (x) = 2x and g (x) = 3x² + 1, find(go g) (x). Show your work using the Equation Editor Tool.

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Q: What is the domain of y =f"(x) if f(x)=;(x-1)*?

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Q: Find the constant a such that the function is continuous on the entire real line. (9x², Flx) = {9x?,…

A: Given function is : fx=9x2    ,      x≥1ax-6   ,    x<1 Here given that function is continuous…

Q: Consider the function y = 3x2+2x-4. What is the exact value of C in the interval [-2, 4] such that…

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Q: Find the slpoe of the secant line between the values x 1 =-1 and x 2 =3 for f(x) = 8x - 3

A: Givenf(x)=8x-3x1=-1  x2=3

Q: 3. If f(x) = 2x + 5, find f(-1) %3D a) Using evaluation: fo-2x +5 b) Using graph:

A: Given,          fx=2x+5

Q: Without using Calculus, determine whether the two variable function f(x, y) = 5x2 − 4xy + 5y2 has a…

A: The given function is f(x,y)=5x2-4xy+5y2

Q: Show that the function f (x) = x* + 3x + 1 has exactly one solution in the interval [-2, -1].

A:

Q: a) Determine the domain and range of the function z = 4 - V9 - (x² + y?).

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Q: What is the linear function of f(x)= -1/2x

A: Linear function

Q: Use the Intermediate Value Theorem to show that f(x) = 2x3 − 3 has a zero in the interval [1, 2]

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Q: Find the point of dimminshing returns (x,y) for the function R(x)=4000-x3+48x2+500x, 0<x<20, where…

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