2. Given the functions f(x) = x² – 2x, g(x) : find the following functions and their corresponding domain, if needed. 1 and h(x) = x² – 1, x +1 - i. (f + g)(x) ii. (h · g)(1) iii. (h o h)(x) iv. (t) f(x + Ax) – f(x) | v. Ax

Q: Given 3y = x^3 + 3x^2 - 9x + 3, Find the relative extrema of f by applying the second-derivative…

A: Given ,  3y=x3+3x2-9x+3. Let y= f(x) Above equation can be written as     y=x33+x2-3x+1     or…

Q: b)f(x) = Vx²

A:

Q: 7. For the function f (x)=(x-2)° +1, a. Sketch the graph of over the interval [0,3].

A:

Q: Given the functions fAx) = x - x and g(x) = x- 1, determine an equation for the combined Ax) y =…

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Q: Find the local and absolute extremum for the functions over their domain: x²+2x-3 4. f(x) : x-2 ||

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Q: 12. For the function f(x) = x² + 10x + 7, x ER, find any global maxima or minima points

A: If y=f(x), then the independent variable x is called the input of the function and the dependent…

Q: 4. Find the values of x for which the line tangent to the graph of f(x) = 3x2 – 4x + 8 has a tangent…

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

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Q: 2 Z= 22,

A: Given  z=2x12+x1x2+4x22+x1x3+x32+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: 1.4 For which values of a ER is the function f(x+ iy) = (a²x – axy) + i ax? + ay an entire function?

A:

Q: Suppose a company wants to introduce a new machine that will produce a rate of annual savings (in…

A:

Q: 1) Find all relative extrema in the function f (x) = x³ + 3x2 – 24x + 12. 2) Find all points of…

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Q: 6. Given the function f(x)=x² find the equation of g(x) where f(x) is shifted to the right 2 units,…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The function f(x) = 2x3 – 39x? + 240x + 9 has derivative f'(x) = 6x? – 78x + 240. %3D f(x) has one…

A: Given data:   The expression for the given function is f(x)=2x3-39x2+240x+9. The expression for the…

Q: A company has determined that its price-demand function for its sale of its product is given by…

A:

Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

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Q: ) Find the values of the constant a so that the function f (x) will be continuous for all x. fax +…

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Q: 3) Let f (x) = e=x² Where is y'> 0? What does this tell you about the original function?

A:

Q: For the function f(x) = x³ – 27x, its local maximum is which occurs at ( its local minimum is which…

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Q: 17. Given the function f (x) = x2 + 2. Find and simplify the difference quotient. S(x+h)-f(x) h 0

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: If f(x) is a differentiable function such that f'(-2)=-1 and g(x)=f(3x+1), then what is g'(-1)?

A:

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: The function g is difirentiable and satisfies g(-1)=4 and g'(-1)=2. what is the approximation of…

A: given g(-1)=4 and g'(-1)=2.         g(-1.2)=?

Q: 12.x + 5x2 + 1 11. Determine the horizontal asymptotes of f(x): V16.x6 +6 1 12. Use the definition…

A:

Q: 3. Consider the following functions: f(z)) = x² + 16 9(=)) = (x – 16)² h((x)) = (x + 1)² – 16…

A: Given: f(x)=x2+16g(x)=(x-16)2 and h(x)=(x+1)2-16

Q: 21. Suppose f(x) = A and g(x) = v2*. Find the x-value for which the two functions are equal.

A:

Q: 1 Find the linearization of the function f(x) = 5x+4 atz-1.

A: The given function fx=15x+4 at x=-1

Q: For what value of c is the function f(x) = = C= C 7 2-4 (x+2)(x-3) x==2 x = 1 otherwise continuous…

A: Given :fx=c,      x=-27,        x=1x2-4x+2x-3   otherwise

Q: For what value of the constant c is the .! function f continuous at x-3 |cx – 2 , if x 3 2 -1 -2 1

A: If function is continous then,limx→n+ fx =limx→n  fx = fnat point nso at given point x=3limx→3+ fx…

Q: The function h(x) 1 can be expressed in the form f(g(æ)), wher x + 4 defined as: f(x) =

A: The function h(x)=1x+4 can be expressed in the form f(g(x)), where g(x)=x+4 We have to find f(x) = ?…

Q: 8. Given the function h(x)=Vx² - 4 +Vx+2, find h(2), h(0), and h(-x).

A: h(x) is given. We have to find h(2), h(0) and h(-x)

Q: 3. Suppose that for a company producing r face shields per week, the cost (C) and revenue (R)…

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Q: The derivative of g(x) = (1/2)* is: positive for all x O negative for all x negative for x >0 and…

A: Given function is gx=12x  ....1

Q: 8. Analyze the differentiability of the following function: f(t) = Vx² – 2 State the restrictions in…

A:

Q: For the function f(x)=x^3/3 - x^2 - 24x +19 iv) what is the range of values over which the function…

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Q: 21. Suppose f(x) = G and g(x) = v2**. Find the x-value for which the two functions are equal.

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Q: If f(x) = 2+|x-3| for all x, then the value of the derivative f'(x) at x= 3 is (A) -1 (B) 0 (С) 1…

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Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x? – 12x + 5 b) Determine…

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Q: if x 2 1. Determine the constant k such that the function f(x) = is continuous at x = 2.

A: As per guidelines, I can answer maximum one question. Since you have asked for multiple questions,…

Q: (b) For what values of the constants c and d is the function continuous and differentiable for all…

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Q: 1/ Find the domain of the following functions : 1 1) f(x, y) = x²+y²+z²+16 2) f(x,y) = In(9 - x² –…

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Q: What is f (2) if the linearization of f (x) at a = 2 is L(x) = 2x + 4?

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Q: 10 Q4 For the functions f(x) = 7x + 4, h(x) =-3 and g(x) = 3x-2 (a) Evaluate (1) g(4) (ii) h{g(4)}…

A: It is given that fx=7x+4,  hx=10x-3,  and  gx=3x-2. (a) Evaluate: (i) Find the value of g4.…

Q: 1 Use the functions given by fx) 1 and g(x) = x' to find (fº g)¯- %3D X - 125

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Q: Find the value of constant K that makes the function below continuous at x = 4. x2 - 4x X< 4 f(x) =…

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Q: Find the local and absolute extremum for the functions over their domain: 2. f(x) = x3 + 4x2 – 11x –…

A: Given function is  f(x)=x3+4x2-11x-2

Q: 9. If f(5) = 13, f' is continuous, and f'(x) dx = 16, what is the value of f(6)?

A: Use property of definite integration

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

A: