(x + 3)³ 12 16 11 f(x) Consider the function 4(х — 1)2 4 1 (x – 1)2 4. Note that - (x – 9)(x + 3)² 4(х — 1)3 24(x + 3) (x – 1)4. f'(x) = f"(x) = and - - 1. Construct a table of signs for f'and f" which specifies the following: (a) the intervals on which the graph of f is increasing, decreasing, concave up, and concave down, and (b) the values of x at which f has relative extrema, inflection points, and vertical asymptotes (if any). (c) Sketch the graph of f with emphasis on concavity. Label all the intercept points, relative extremum points, inflection points, and holes (if any) with their coordinates. Show the asymptotes of the graph of f and label them with their respective equations

Q: Show that the equation Fu 1 u 0x² ² 3t² 0 is satisfied by u=f(x+ct) + F(x-ct) where fand F are…

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Q: 5. Let f(x) = x² + 3x and g(x) = 2-x. (a) Find (f - g)(x) (b) Find (fg)(2) (c) Find (4) (x) and its…

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Q: 13. (a) Find the inverse of the functio x) = 2x – 5 (b) Find f- (3)

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A: we have to differentiate two times of f(x) ,where f(x) is given by

Q: 2x x - 3. a) Find the domain of the function: [-3, ∞0) (-∞0, 3] (-∞, 3) U (3, 0) (0, -3) U (-3,0) 2.…

A: According to bartleby guidelines we supposed to do the first subparts of multiple subparts kindly…

Q: 11) For the function f(x)x+3 a) Find f(1) and f(m +6) b) Find the domain

A: We have been given a function and we are supposed evaluate its value for the given value/expression…

Q: АСTIVITY 2 Direction: Read each instructions carefully and answer as required. A. Differentiate the…

A: hello greetings from bartely.i am here to help you

Q: 3) Find domain of the following functions х+4 a) f (x) = х2+2х-8

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Q: 1. Assume that the function f is a one-to-one function. (a) If f(2) = 5, find f-(5). Your answer is…

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Q: 3) g(x) = x + 2 f(x) = x³ + 4x Find (g · f)(x) А) бх* - бх3 + бх? - бх 2x + 4x2 – 8x 4) f(x) = x² –…

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Q: 10. (a) Describe the transformations of y = x³ into the function f(x) = 8(x-1)³ -5. = (b) Describe…

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Q: 1. Determine f'(x) and DO NOT simplify. f(x) = 2x³7x² + 3x - 1 a) c) f(x) = -3√x 2 b) f(x) =…

A: To determine f'x and to do not simplify. (a) fx=2x3-7x2+3x-1 (b) fx=5x2-3x (c) fx=2x2-3x

Q: For the function f(z) 2(x – 5) + 7, which of these equations describes f '(r), the inverse of the…

A: We wil use concept of inverse function to find the answer.

Q: 32. For the function f(x) = 3X *5 Find: f (0) f(-2) f (3)

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Q: 7. Consider the functions f(x) = 2x² - 7x + 4 and g(x) = -7x + 5. a) Find f(-1). b) When does g(x) =…

A: Function is f(x)= 2x2-7x + 4 .............(i) We've to find the Value of f(-1) Put the Value of x=…

Q: 5) For functions f (x) = x² – 15x + 45 and g(x) = x - 9, find |(x)

A: f(x)=x2-15x+45, g(x)=x-9, (fg)(x)=?f(x)=x2-15x+45  g(x)=x-9  Now fgx=f(x)g(x)             [Quotient]

Q: Differentiate the following functions using product rule. 1. f (æ) = (3x – 9) (x – 6) 2. ƒ (x) = (æ³…

A: The product rule of differentiation is given by: ddxf.g=dfdx.g+f.dgdx

Q: The following table gives the number I = I(t), in millions, of adult Americans with Internet access…

A: here we can use table to solve this question.

Q: Consider the function f(x) = 2x - 1/ x+3…

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Q: Find the f(x) =3-2x2+x by finding F(b)- fCa) averoge rote st change of the function b-a where a=l…

A: a) The given function f(x) is, f(x)=3-2x2+x The average rate of change of a function in the interval…

Q: 6. The starting point of f(x) = -23(x – 4) – 8 is А. (2,-8) В. (4,8) С. (-4,-8) D. (4,-8)

A: To find the starting point of a function, first, we find the domain of the function. The starting…

Q: Determine the domain of the following functions: За — 6 a) a(x) b) b(x) = /5 – x c) c(x) = 3x4 –…

A: We can find the domain of the given functions as below.

Q: The critical point of the function f(x) = x³ – 5x² + 2x – 17 is %3D - o (용, 1) ㅇ (름, 1) o (음,-1) (금,…

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Q: Question Let f(x,y)=1 √x+9-√√√x+9 x-y E if x*y if x=y then f(x,y) is continuous at (0,0) if:

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