Consider the graph of f(x) below. Over what open interval is f'(x) positive? Give your answer in interval notation.

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.…

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Q: 6.) Use the limit definition of the derivative to find f' (x), given f(x)=x-3 x+5

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A: From the graph of function f'(x), number of roots of f'(x) are three. Let f'(x)=ax3+bx2+cx+d

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Q: Find the derivative of a function at a certain number using the formula f(x) – f(x1) x-X1 x- x1…

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Q: g(x) = In tanh-1 x

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Q: Use the graph of the first derivative function  f'(x) to find the interval  on which function is…

A: Given: the graph of the first derivative function  f'(x).

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

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

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Q: 3. Below is the graph of y = f'(x), which is the derivative for some function f. Using the graph of…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

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Q: Let f(x) = 2x2 + x. Determine f'(1) using the definition of the derivative as a limit.

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Q: 51. Is the function given by G(x) 1 continuous at x = 0? Why or why not?

A: Given: Gx=1x To check whether the given function is continuous at x=0

Q: Sketch the graph of f(x) = sin¬'(x² + y²) by analyzing its level curves.

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Q: For which values of x is the function below NOT continuous?

A: To find out the values of x at which the function is discontinuous.

Q: Given the graph of derivative f'(x), find: a) Any interval(s) where f(x) is decreasing b) Any…

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Q: 49. Is the function given by g(x) = x² 3x continuous at x = 4? Why or why not?

A: Given: g(x)=x2-3x Determine the limit at x=4. limx→4g(x)=limx→4(x2-3x)

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Q: Sketch the graph of the derivative for function shown.

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Q: How is the graph of g(x)=2sin(3x) related to the graph of f(x)=sin x? GRaph the function g(x), show…

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Q: Suppose the derivative of f is f'(x) = (x + 1)*(x - 2)*(z- 3). On what interval is f increasing?…

A: A function f(x) is said to be increasing in an interval of it's derivative is positive in that…

Q: Is the function given by g(x) = x²-3x continuous at x = 4? Why or why not?

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Q: Sketch the graph of f(x) = x lxl. Then show that f '(0) exists.

A: A function is a relation which maps each value in domain to exactly one value in range.  For a…

Q: Find the derivative of the function by the limit process. g(x) = -398 g'(x)=

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Q: Use the e - S definition to show that the function x- 1 f(x) = x +2 %3D is continuous at x = 3.

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

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Q: The first derivative of the function h is given by h' (x) = x³ – 3x2 + x. What are all intervals om…

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Q: The graph below is of f "(x) for some function f(x) with domain (-∞, ∞) (i.e., the graph of of the…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the…

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Q: 3. Let f be defined by f(x) = e* sin x. What is the slope of the line tangent to the graph of f at x…

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Q: 1. Let f(x) =1. Using the limit definition of the derivative, find f'(x).

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

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Q: Let f(x) = /3x + 4. f(x) – f(a) Using the definition of derivative at a point, f'(a) = lim х — а…

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Q: Let f(x) = V5x + 2. Find the derivative f'(x) using the limit definition.

A: We have to find derivative

Q: The derivative of f with respect to x of f(x) = In x° is

A: Since, you have posted multiple questions. As per guidelines I"ll solve only first question. If you…

Q: Suppose that g: R →R is a differentiable function, with derivative g'(x)=(x – 1)·(x – 2)² - (x – 3)³…

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Q: On the graph of f(x)=sinx and the interval [0,2π), for what value of x does the graph cross the…

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Q: 2.Given f(x)=5Vx-1, find f'(x)using the limit definition of the derivative.

A: Given f(x)=5x-1

Q: 13. Sketch the derivative f'(x) for this graph of f (x):

A: Graph drawing of f'(x) problem...

Q: What is the derivative of f(x) = 1 over x⁵

A: here we use the formula of derivative  ddxxn=nxn-1

Q: Let g be a function that has derivative x(x – 3) (x – 5)e2" g'(x) = Does x=3 belong to a local…

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Q: A graph of yY = f(x) is shown. In the same coordinate system, sketch a graph of the derivative func…

A: when a line passes through two given points, say (x1, y1) and (x2, y2).  the equation for this line…

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

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Q: Select all of the graphs that depict a function which is not differentiable at x=0.

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Q: What value should be assigned to f(2) so that the extended function is continuous at x=2

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Q: 3. Use the graph of y = f (x) shown to sketch the graph of its derivative f'(x). [if on your own…

A: Give function f(x) has graph If you see this graph you will observe that derivative of f(x) will be…

Q: Suppose that f is a function defined as f(x) = xª . drawn to the graph of f at x = 1. Use exact…

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