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

Q: 1. Consider the function f(x) = x6 - x³. a. Determine the absolute extremum using the First…

A: The given function is fx=x6-x3. a. Find the absolute extremum using the first derivative test. b.…

Q: 7. Let f be a function that has first derivative f /(x) = +2 and second derivative f"(x) = 2-2++2.…

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Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

A: Given   y = sin (x3) ....(1)   , (1, 2)

Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Critical points of the function are the point either the derivative is not defined or derivative is…

Q: Sketch a graph of the function f(x) 2 sin(2x). %3D -77/8-31/4-5n/8-/2 -3/8-7/4-T/8 t/4 3n/8- /25/8…

A: Given function is f(x)=-2sin(2x)We know that period of sin(x)=2πThe period of sin(2x) will be π and…

Q: Prove, without graphing, that the graph of the function has at least two x-intercepts in the…

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Q: 67. Is the function given by g(x) 1 continuous over %3D x + 5 the interval (-4, 4)? Why or why not?

A: g(x)=1x+5

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: 5. Show that the function f(x)= 3x-9 is not differentiable at x=3. Find the formula for f'(x).

A: To Prove: Show that, given function is not differentiable at x = 3.…

Q: Consider a function f with domain (xx 0} and the following derivatives: f(x) = bx-1 and f (x) = bx…

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Q: Discuss the continuity of the function on the closed interval.

A: Given: f(x)=x2-1x+1 The function is continuous at a point if the function returns a unique value…

Q: Select the graph of the given function and determine the interval(s) for which f(x) > 0. Ax) = 16 –…

A: For f(x) = 16 - x² * Since coefficient of x² is negative, Therefore the graph of the parabola of…

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: The function In x f (x) = x2 is Select one: increasing on the interval (-o, -) and decreasing on (5,…

A: fx=lnxx2 The domain of given function is 0, ∞. Differentiating with respect to x, we get…

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given: f(x)=x29-x2 To Find: Intervals of increasing and decreasing on (-3,3). Concept: (a). if…

Q: Here is the graph of the function h(x)on the interval (-5, 5), and part of a line tangent to h(x) at…

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

A: Proceed as shown below

Q: 6. Find the absolute extrema of the function on the closed interval given: f(x) = 2x/2 – x; [ –2,1]

A: Pue derivative zero, if value lie in interval then put in function for maxima and minima

Q: Is the function f(x) : 1 continuous or discontinuous on [2,+∞)? Vx - 2 Is the function f(x) : 1…

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Q: 1 Sketch a graph of the function f(x) = 3 sin 5- 4- -87T -7 -6I -5 -47T -37 -27 27T 37T 47T -2- -3…

A: the amplitude of the function is 3 the time period of the function is  2π1/4=8π

Q: A Function f(x) is defined for all xr>0, and satisfies f(x2) = x3 for all x > 0.Show that f is…

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Q: Let g be a function that is defined for all x, x 2, such that g(3) = 4 and the derivative of g is x²…

A: The interval where second derivative of function is positive, is the interval where the function is…

Q: and the domain of the function using interval notation. To enter ∞o, type infinity. To enter U, type…

A: We can solve this as follows:

Q: Consider the function f(x) = 7x + 5x-¹. For this function there are four important intervals: ( ∞,…

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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: 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: The function f(x) = 3 x4-4 x3-12 x2 +1, is decreasing on the interval OA (-00,-2)U(0,2) OB…

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Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

A: Solve both the problem in the following way:- (i) given point will satisfy the function. (ii)…

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

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Q: Find the intervals on which the function f(z) = z' - 6z + 10 is increasing and decreasing. %3D

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Q: 3-The function f defined by 2. Is f is Continuous at x=| ?

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Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

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Q: 12. Suppose we know that f (x) is continuous and differentiable on the interval [1,9], that f (9) =…

A: To find: The largest possible value of f1. Given: The fx is continuous and differentiable on the…

Q: Suppose the function ) has a domain of all real numbers except x-8. The first derivative of fx) is…

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Q: Consider the function f(x) = 8x + 4x¯. For this function there are four important intervals: ( – ∞,…

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Q: (1) Find and classify the extreme values of f(x) =6x* -4x over the interval [-2,2].

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit…

Q: 14. Find the end behavior for f(x) = -x - 4 A. x- +o, f(x) +0 x--o, f(x) - +0 B. x- +o, f(x)-0 x-…

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: The function f is continuous for all real numbers and the graph of its derivative function f' is…

A: Given The graph of the derivative of a continuous  f

Q: If a function is real and continuous in the region from a to b and f(a) and f(b) and if both have…

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Q: Suppose f(x) is differentiable everywhere and f(-3) Show f(1) > -6 and f(-5) -2.

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Q: 2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) =…

A: Given, f'x=21-x21+x2                         ...(1) and f''x=4xx2-31+x22

Q: 1 Discuss the continuity of the function f(x) on the interval (0,2] and [-1,3] x2 -4

A: A function f(x) is said to be continuous in the closed interval [a,b] if→ f is continuous on (a,b).→…

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

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Q: What is the graph of a function f that satisfies the conditions: f' (x) > 0 on (-∞, –1) U (–1, ∞)…

A: f'(x)&gt;0 on (-∞,-1)  U (-1,∞) when second derivative is positive then the function f(x) is…

Q: 11. Determine the absolute extreme values of f(x) = xe-/2 = xel-/2 on the interval [0, 5].

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Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

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Q: Show that the function f(x) = |x-3| is not differentiable at x = 3.

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