Suppose the function f has a domain set of all real numbers. Given below is the graph of f(x). f'(x) + > x -4 13 -2 -1 1 2 4 5. 6. Which of the following intervals or union or intervals is the function f increasing? A (- 00 , - 3) U (1,5) В (- 00, - 1) U (3, + o ) (-3,1) U (5, + 0 ) (-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: 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: 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: 13. Find the end behavior for f(x) =x- 2 A. x- +0, f(x) - +o x--o, f(x) → - B. x +o, f(x) - +0 x--o,…

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

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: x²-1 If f(x) = for x +1 and f(x)=2 when x 1, show that the function x-1 is continous at x=1?

A: Show that f is continuous at x=1

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: 20. Suppose that f(x) is continuous and differentiable on the interval [-3,0], that f(-3) = -7 and…

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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: 10- Continuity of the function f(x){*-5 -1<x<2 x² -1 2< x< 3 at x=2?

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

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

A: Proceed as shown below

Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x +1 on [-1,3]

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Q: 4. Verify Rolle's Theorem for f(x) = x² – 2x + 1 on [-1,3]

A: Verify Rolle's theorem

Q: ,for x 1 Discuss the contuniuty of f andf'.

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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: Use the definitions of increasing and decreasing functions to prove that       f(x) = x3 is…

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Q: +1 Differentiate the function f (x) = In +1

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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: Suppose g is the function defined by picture where k and m are constants. If g is differentiable at…

A: Solution

Q: What is the intervals to its corresponding function which have at least one real zero. f (x) = 202 +…

A: Given query is to find the interval where function has atleast one real zero.

Q: Let f(x)=x²+2x if x<5 - Cx if x 25. For what value of the constant c is the function f continuous on…

A: We have to calculate the value of c

Q: Consider the function f(x) = 5x + 8x-. For this function there are four important intervals: ( – 0,…

A: Critical points are where f'(x) =0 and function is not defined where f(x) is not defined.

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

A:

Q: 4. Verify Rolle's Theorem for f(x) = x² - 2x +1 on [-1,3]

A: Given the function f(x)=x2−2x+1 On the interval [−1,3]

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

A:

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: Suppose f is differentiable with f(0) = 0 and 0 0.

A:

Q: 5. Discuss the continuity of the function x'- 1 f (x) = { 2, **- 1 at x = -1. x+2 2, x=- 1

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Q: 5) Show that the function f(x)=-÷+1 below is continuous at x = -1. x-1 2- -3 -1- -2 1.

A: A function f(x) is continuous at x=c if  We have to show that is continuous at x=-1.

Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): f(x) = m= n= 4 x-2 mx² - nx 2x -…

A: Topic- Limits and continuity

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: Consider the function f(x) = 12x + 45x4 – 200x³ + 5. For this - function there are four important…

A: The given function is: fx=12x5+45x4-200x3+5 To find the critical points of this function, first,…

Q: Verify Rolle's theorem for f(x) = x² - 9x +6 over the interval [0, 3].

A:

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

A: We are given the function for which we need to find the stationary points f(x)=7x+5x-1

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

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

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Q: Draw a function F(x), defined for all real numbers x, that satisfies the following properties.…

A: The first derivative is everywhere positive and the second derivative is everywhere negative