Suppose the functionf has a domain set of all real numbers. Given below is the graph of f(x). f'(x) ... -4 В -2 -1 1 3 4 5 Which of the following intervals or union or intervals is the function fincreasing? (- 00, - 3) U (1,5) B (- 0, -1)U (3, + ) 6. 2.

Q: Which of the following is the absolute minimum value of the fuk took f(x)=(x-3)^3 on interval [1,4]

A: The graph is shown below:

Q: For which interval is the function f(x)=x√√4-x² continuous O (-∞, -4] and [4, ∞) O (-∞, -2] and [2,…

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Q: Suppose f'(x) = x² - 1. Then the graph of f is concave upward on 0 (-∞0,0) O (-1,1) (0,00) O (-∞,…

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Q: Suppose that the function f is defined on the interval (-2, 2 as follows. -1 if-2<x<-1 if -1<x<0…

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Q: f(t) = 3 – 9 ? -6, [-3, 3]

A: To find: The continuity of the function f(t)=3-9-t2 on the interval [-3, 3]

Q: Suppose that the function f is defined on the interval (-2.5, 1.5) as follows. -2 if-2.5 <x-1.5 -1…

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Q: Suppose that the function fis defined, for all real numbers, as follows. -x+2 if x1 Graph the…

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Q: 10 The function f(x) = - has a removable discontinuity at x = 2. To remove the - 2 discontinuity,…

A: Given: f(x)=10x+x2−4x−2

Q: 3. Consider a function f(2) that is analytic in a domain that includes the real axis. When z is…

A: Given that,                 fz is an analytic function in a domain that includes the real axis .  We…

Q: Suppose that the functionf is defined for all real numbers as follows. +1 if x1 Graph the function…

A: Given :   Fx = x2+1              x&lt;12                     x=18-3x              x&gt;1 To find :…

Q: 2. Determine whether the function y= -x5 + x3 – 1 is even, odd, or neither. Justify your ans wer.

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Q: Find an example of a function on the real line, R, that is contin- uous everywhere except at x = on…

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Q: Suppose that the function f is defined on the interval -2, 2) as follows. -2 if-2<x<-1 -1 if-1<x<0…

A:

Q: Suppose that the function f is defined on the interval [-2, 2) as follows. -2 if -2<x<-1 -1 if…

A: It is given that,   f(x)=-2  if -2≤x&lt;-1-1  if -1≤x&lt;0 0    if  0≤x&lt;1 1   if  1≤x&lt;2 We…

Q: If f(x) < 0 for all real numbers x then f is decreasing on (-o, 00).

A: Proceed as shown below

Q: Suppose that the function g is defined on the interval (-2, 2] as follows. -1 if -2<x<-1 if –1<x<0 g…

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Q: 7 Find the most general function F such that F'(): - 5V?.

A:

Q: What is the function f on (a, b) if for all x1, X2 in (a, b) when x, f(x2). is it decreasing or…

A: for all x1 , x2 in a,b when x1&lt;x2 then fx1&gt;fx2 claim- is it decreasing or increasing

Q: Suppose that the function h is defined on the interval (-2, 2 as follows. -1 if-2<xs-1 if -1<x<0 0.…

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Q: 9. If f (x) = prove that f (xr) is an even function. et -1 2

A: A function f(x) is said to be even if we have f(-x)=f(x)

Q: 1 Discuss the continuity of the function g(x) : on the interval [-1,2]. x2-4

A: Consider the given function and interval, f(x)=1x2-4 and [-1,2]   Now, check the value of the…

Q: the Domain (Dr) and Range (Rr) of the following function 4 f(x)=; V25-x4 O Df=[-5,5], Rf=[-2/5,…

A: The domain is a set of x-values where the function is defined. In other words, the domain is the…

Q: Suppose that the function h is defined on the interval (-2, 2 as follows. (-1 if -2<rs-1 if –1 <x<0…

A: Solve the function

Q: Suppose that the function f is defined on the interval -2, 2) as follows. -2 if-25x<-1 -1 if -1Sx<0…

A: Function value at a given point

Q: Let f(x) be an EVEN function. If the point (2, 3) belongs to f, then another point likely to belong…

A: Let f(x) be an EVEN function.

Q: 4 If f(x) = x 2 - function for all real values of x, then f(8) is equal to

A:

Q: 4. Consider the functions g(x) = and . Determine (12)- (}),

A:

Q: Select the graph of a function f that satisfies f' 0 on (-0, -1)U(-1, 0).

A: means f is decreasing for x&gt; - 1   means f(x) is concave up on both sides of x=-1

Q: - Find f (x) given f' (x) 6x2 - 4x + 3 and (2, 15) is on the curve of f (x) .

A: To find the function from derivative we need to integrate.Here we will integrate to find f

Q: Suppose that f(x) is a differentiable function such that f(3)= 8 and f'(3)=-2. If g(x)=xf(x), then…

A: Product Rule of differentiation : d(u.v)dx = u.dvdx + dudx.v

Q: Suppose that the function h is defined on the interval-2, 2) as follows. -2 if-2<x<-1 -1 if-1<x<0 h…

A: Given:     To determine: h(-2), h(-1.5), h(1)

Q: The piecwise function g(x) is defined by x + 2 when x 1. What type of discontinuites are present in…

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Q: A portion of the graph of a function f (x) with domain (-∞, 0) is shown. to- The functionf has…

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Q: Suppose that the function g is defined on the interval (-2, 2] as follows. 1 if-2<x<-1 0 if - 1<x<0…

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Q: If f(x)<0 for all real numbers x, then f is decreasing on(-♾,♾) True or false

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Q: Consider the function f(x) = 2/x + 2 on the interval [4, 8]. Find th function on this interval.

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Q: Which of the following is true about the graph of f(x) = 3/(x+1)? a. It is continuous on (-6,-1]…

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Q: Select the graph which satisfies all of the given conditions. f' (-3) = f' (1) = 0 Increasing on…

A:

Q: Find the are under the graph of f(x) = 4-x2  on the interval (-2,1)

A: Given, f(x) =4-x2  we have to find the area under the curve on the interval (-2,1)

Q: Sketch the graph of a function f(x) that satisfies all of the following conditions. f(-3) = 1, f(2)…

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Q: Which of the graphs of f(x) below have the following properties? • f (x) > 0 on (b, d) and (g, ∞) •…

A: we know that when the derivative of a graph is greater than zero then the graph of f(x) increases…

Q: Show that Rolle’s theorem is false for the function f(x) = |x| on the interval [−2, 2]. How can a…

A: Given function f(x)=|x|interval [-2,2] We apply Rolle's theorem only when the function is continuous…

Q: Determine where the graph of the function f(x)= 2x-V49-x is concave upward and where it is concave…

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Q: The graph of the second derivative, f"(x), is given. > 10 6 -1 -2 -4 -6 -8 -101 Determine the…

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Q: Find the discontinuities of the function 2х — 1 - if 2 < x x +1 1 Let G be the function defined by…

A: Given,

Q: On what intervals is the function f(x) = x-4r both decreasing and concave up? Write your answer in…

A: fx=x4-4x3 Differentiating with respect to x, we get f/x=4x3-43x2    ∵dxndx=n·xn-1=4x3-12x2 Again…

Q: Show that there exists an x in the interval (0, 1) that satisfies the given equation V = 1-x Hint:…

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Q: 5. Find the value of k that makes the following function continuous. f(x) : ={2x - 1,if x2-1

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