Suppose the function f has a domain set of all real numbers. Given below is the graph of f(x). f'(x) ... -4 3 -2 -1 1 3 4 5 6 Which of the following intervals or union or intervals is the function f increasing? A (- 00, – 3) U (1,5) B (- 0 , – 1) U (3, + ∞ ) (-3,1) U (5, + 0 ) D (-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: 1.) Determine the largest interval over which the function flx) = \x+3 is continuous. 2x 2.)…

A:

Q: Suppose f(x) = x° + 3x + 1. In this problem, we will show that f has exactly one root (or zero) in…

A: Please see the below picture for detailed solution.

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

A:

Q: The function f(x) on [0, 3 has x2 + 1 absolute maximum is 0.3; absolute minimum is 0 absolute…

A: The given function f(x)=xx2+1 Differentiate the function with respect to x.…

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: 22. The function f(x) = Vx – 6 is transformed according to (x, y) → (7x – 7, - y+1). the transformed…

A: Substitute fx for y in the transformation and simplify. x,y=x,f(x)→7x-7,-f(x)+1=7x-7,-x-6+1

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: 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: The value (x, f(x)) of the maximum or minimum limit of the function 8 + f(x) = x3 - 6x2 + 4x and for…

A: Please see the attachment

Q: Sketch an odd function with a positive leading coefficient having all of the following features:…

A: We have to draw graph of given odd function.

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: 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]

A:

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

A: Verify Rolle's theorem

Q: The function f has a continuous second derivative, and it satisfies f(-6) = -1, f'(-6) = 0 and…

A: Maxima minima problem....

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

A:

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

A:

Q: 15. Given , find f- (x) = Vx+ 7 and the domain of f-1 (x). Of-" (x) = x³ +7 with domain for f-l (x)…

A: In the question we have to find inverse of the given function and domain of the function.

Q: The limit represents the derivative of some function f at some number a. State such an f and a. 16 +…

A: This question is about differentiation expressed as limit of a function

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

A:

Q: x3 – 7x2 + 5x + 7 = 0, (-1, 1) Let f(x) = x3 - 7x2 + 5x + 7. f(x) is ---Select--- f(-1) = on the…

A:

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: 5) Suppose that f is the function implicitly defined by the equation + tan ( In = evi near the point…

A: Given:       x+y4+ Tanin xy = ey   →1    near the point ( 4, 4 ) eTo Determine: f is an increasing…

Q: 8. Determine the natural domain of the function Vx–1 f (x)= x²-3x+2 in interval notation.

A:

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

A:

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

A:

Q: 1. Let f(x) = 4x − 4x 2 . Verify that f(x) satisfies the conditions of Rolle’s Theorem on the…

A: Note:- According to the company policy we can attempt ?️ only one question so please upload the next…

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

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: 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…

A:

Q: Find a function such that f'(-1)=1/2, f'(0)=0, and f''(x)&gt;0 for all x, or prove that such a…

A: Given that f"(x)&gt;0 for all x and f'(-1)=1/2, f'(0)=0 Since f"(x) exists for all x, so we can say…

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

A:

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

A:

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

A: