Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x-4 s(x) = 4x+2 Enter your search term Write the expressions for (r-s)(x) and (r+s)(x) and evaluate (r-s)(2). ()(+) = [| %3D (++ +)(+) = 0 X 5 ? (--)(2) = 0 I Don't Know Submit

Q: Show that f(x) = x3 - 2x - 1 has a real zero between 1 and 2.

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Q: Find the critical numbers of f(x) = x 3/5  (4 -x )

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: 1. If the leading coefficient of an odd-degree polynomial function is negative, then the function…

A: Check the end behaviour of the function as x tending to minus infinity and infinity.

Q: 9. For |x|<1, prove that 8x 16x 24x 1-x1+x 1-x 2 8x 8x = 1+ (1 – x)? (1+x2 (1-x)? ...

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Q: The function f(x) = 2x³ - 39x² + 216x 3 has two critical numbers. The smaller one is x = and the…

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Q: 2. If the polynomial f (x) divided by (x – 3) gives a remainder of -1, then the remainder of…

A: Solution is given below:

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(0) = 0

A: Given: f(0)=0

Q: 4. Find the absolute maxima and minima for f(x) = 4x - 9x2- 12x-1 on the closed interval [0, 4].

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Q: 5. Check the continuity of r+5| 2x+10 x + -5 f(x) = x = -5 at x = -5.

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Q: find the critical number: F(x) = x^4/5 * (x-4)^2

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Q: Find the critical numbers of the function. f(x) = 3x + 4x3- 12x2 %3!

A: Given function is f(x)=3x4+4x3-12x2. The critical number of a function f is a number c in the domain…

Q: Find real zero of f(x) = x* – 2x³ – 4x² + 4x + 4 within TOL = 10-5 by following methods:

A: First, plot the curve for f(x). Use the graph to find a real zero as mentioned in the question.…

Q: Explain why the function is discontinuous at the given number a. (Select all that apply.) x2 - 4x if…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find all critical points for f(x)=x²-x² - 2x + 1.

A: Our Aim is to find all the critical points for f(x)=x3-12x2-2x+1 -(i)

Q: In the function:  f(x)= 6/((x^2)-16)  What are the critical numbers of the function?  When is the…

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Q: Show that when x increases from 1 to 1.25 and when it increases from 2.75 to 3, the value k of grows…

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Q: Find the critical numbers of the function.   f(x)  = 2x3 - 3x2 -36x

A: Critical numbers are the numbers for which f'(x) = 0

Q: Find the critical numbers of the function.…

A: Critical numbers : f(x)=4x2-6x The derivative of the function is f'(x)

Q: how many critical numbers does the funtion f ( x ) = | x 2 − 5 | have?

A: The graph of the function given below.

Q: Find Absolute Extremums of F(x)=2x^3-6x over [0,3]

A: To find the absolute extremums of the function F(x)=2x3-6x over [0,3]

Q: 1. f(x) = 3x + 4, at x = 4 2. f(x) = 3x2 – x + 2 at x = 2 3. f(x) = ***, at x = 1 x+3 4. f(x) = X-1…

A: As per guidelines we can solve only three subparts at a time, so the first  three subparts can be…

Q: Find the local extrama of f(x)=x²-8x+12 on a closed interval [-2,5] O a. minimum value at x =4 is -4…

A: Topic- application of derivatives

Q: Show that f(x) = x5 +2x4-6x3+2x-3 has a solution between 1 and 2. Use the intermediate Value…

A: The equation given to us is  f(x) = x5 +2x4-6x3+2x-3

Q: Using Taylor's theorem, formally represent 2x° +x* – 3x³ +x² – 5x +1 as x+1.

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Q: 5.5 (a) Determine the roots of f(x) = -12 – 21x + 18x2 – 2.75x3 graphically. In addition, determine…

A: Given: f(x)=-12-21x+18x2-2.75x3 To determine: Root of given function by a) graphing method. b)…

Q: Find all critical numbers of the function f ( x ) = 4 x 3 + 6 x 2 - 72 x + 9

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Q: (a) Show that (x2 + v2x + 1)(x² – v2x + 1) = x* + 1.

A: Given that: (x2+2x+1)(x2-2x+1)   NOTE: As per our answering guidelines, we can only answer 1…

Q: If f (x) =x2-6x+2, find the maximum and minimum values of f on the closed interval [-3,4] Oa f (x)…

A: To find: The maximum and minimum value of the function is fx=x2-6x+2. Concept used: Power rule of…

Q: The Taylor polynomial of degree 100 for the function ƒ about x = 3 is given by (x – 3)100 50! 2n…

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Q: Find the critical numbers of f (x) = x2/3-x

A: We will differentiate the function and equate it with 0. We will again differentiate it to check the…

Q: g(x) = x' + 3 x² – 24 x

A: The point x=k is said to be the critical point of the function f(x) if Case 1 : f(k) exists and…

Q: f(x) = x3 + 5x² + 2x

A: Given: f(x)=x3+5x2+2x

Q: The sum of all the critical numbers of the function f(x) = x4 - 10x2 is what

A: Given function is fx=x4-10x2 To find the critical points we differentiate the given function with…

Q: Find the critical numbers of the function. f(x) = x³ + 3x² – 24x

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Q: 4. Find the maximum value of x if f(x)=6cos(x)-3x²-2x. Using Quadratic Interpolation with a relative…

A: Solution...

Q: Sketchthegraphofy=x2−5x+4.

A: We first make a table for y=x2 −5x+4 x 1 2 2.5 3 4 y 0 -2 -2.25 -2 0

Q: Find any critical numbers of the function. 1(x) = x* - 4x 1.)

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Q: 2. What are the critical numbers of the function: f(x)=(x² - 4) A. X=0, x=2 and x =-2 В. X30 only С.

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Q: If the leading coefficient of an odd-degree polynomial function is positive, then the function…

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Q: Find all critical points of f(x) = 2x³ + 2x-. (Use symbolic notation and fractions where needed.…

A: First, we find f'(x) using the power rule

Q: 1. Find absolute extreme values of the function on the given interval. Ax) = x - óx2 + 9x + 1, [2,…

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Q: Find all critical points for f(x)=x²-x²-2x+1.

A: Critical points of the given equation is x=-2/3,1

Q: Find the DOMAIN of 8z-24r-320x f (x) = 7z+28z2-315z Section 3.4 O + -5, 9 O+0,-5, 8 Ox+0,-5, 9 O…

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Q: Use the Intermediate Value Theorem to show that there is a root of the given equation in the…

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Q: Find the critical number of f(x) = 3x^2 - 18x + 4

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Q: 10. Find all of the discontinuities that exist for g(x) = 2*+3x-4 Show any work required to %3D x+1…

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Q: Graph of a function with roots at x=3 that has a multiplicity of 3 and x=-2 that has a multiplicity…

A: We know that if a function f(x) has a root at x0 with multiplicity α then x-x0α is a factor of f(x).

Q: Find critical number of g(x) = x^2 - 8x +9

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Q: What are the critical numbers of the function:   g(x)=36x-9tan(x)

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