Suppose the function f has a domain set of all real numbers. Given below is the graph of f(x). f'(x)

Q: Use interval notation to indicate where f(x)=x-7/(x-5)(x+5) is continuous.   "f" is continuous on…

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Q: f(x) = 9x² - 4 at x = 1

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Q: Suppose f is a function with property that f(x) ≤ x 2 for all x. Show that  f'(0) = 0.

A: Suppose f is a function with property that f(x) ≤ x2for all x. Showthat f'(0) = 0.

Q: Explain why the function g(x) = ln(4-x2) + square root of x+1 is continuous at every number in its…

A: Consider the given function g(x). The function g(x) is the sum of two functions f(x) and h(x).First…

Q: Use interval notation to indicate where x2 – 1 - f(x) = x2 – 7x + 6 - is continuous. f is continuous…

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Q: find the derivative of f(x) = x-3/3x+4 using the limit definition of the derivative. then state the…

A: Consider the given function as fx=x-33x+4. The limit definition of the derivative of a function fx…

Q: Use grahical edition to sketch the graph of f + g.

A: Let the given graphical data be plotted in the form of table x f(x) g(x) f(x)+g(x) 0 1 2 3…

Q: Define f(x) = (x2 - 81)/(x - 9) at x = 9 so that the function becomes continuous at 9.

A: Concept: A definition of a function is that a relation from a set of inputs to a set of possible…

Q: Define f(x) =(x2 - 81)/(x - 9)at x = 9 so that the function becomes continuous at 9.

A: Given function is fx=x2-81x-9. To define function fxso that the function becomes continuous at x=9.…

Q: If the function f (x) is continuous for all real numbers and if f (x) x²-4 when x + -2, then x+2 f…

A: f(-2) = -4

Q: Find f'(x). f(x) = x5 – 2x3 + x – 1 %3D f'(x) = Compare the graphs of f and f' and use them to…

A: Given: f(x)=x5-2x3+x-1 To find: f'(x)

Q: is the function continuous at x=5 if f(x)={x2-4x-5/x-5,     x5

A: Given: f(x)=x2-4x-5x-5  ,   x<5x+1            ,  x≥5

Q: Show that f (x) = 2x2 -3 is an even function. Explain why itsgraph is symmetric about the y-axis.

A: Here given fx=2x2-3   A function is said to be an even function if f-x=fx Now…

Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: sketch to graph the function f(x) = In(x + 2) – 1. %3D

A: f(x)=ln(x+2)-1Now, putting value of x=-1f(-1) =ln(-1+2)-1           [ln1=0]           =0-1…

Q: Show that f (x) = x3 - 3x is an odd function. Explain why its graph is symmetric about the origin.

A: Given, fx=x3-3x

Q: Suppose f is a function with range (-∞, ∞) and g is a function with domain (0, ¤). Is it possible…

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

A: If f(x) is a continuous function, then derivative of the function at point a exits if and only if…

Q: Find the intervals on which f(x) = x(x + 3)(x – 1) is positive by plotting a graph. (Enter your…

A: Given - A function To Find - Interval for f(x)>0

Q: If f(x) and g(x) are two functions defined on an interval then, ꭍ{f(x)±g(x)} is equal to?

A: The sum rule states that the integration of the sum of two functions equals the sum of the integrals…

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: Sketch one possible graph of a function f(x) defined on R that satisfies all the listed conditions.…

A: Plotting Graph.

Q: Find f'(x). F(x) = x5 – 4x3 + x - 1 f'(x) = Compare the graphs of f and f' and use them to explain…

A: Given, f(x)=x5-4x3+x-1

Q: If f(z) is analytic function show that:

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Q: find the intervals on which f(x) is increasing and decreasing. then sketch the graph. f(x) = 7 --…

A: We use first derivative to find out where function increasing or decreasing  when f'(x)<0 then…

Q: Given f(x) = Vx and g(x) = |x – 2|, find 9. Determine the domain of the function in interval…

A: Given function :

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: explain why the function has at least one zero in the given interval. f(x) = x^3+ 5x-3 intervals…

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Q: What conditions must be satisfied by a function if it is to be con-tinuous at an interior point of…

A: A function is continuous at an interior point c of its domain if

Q: An even function is symmetric with respect to the________

A: An even function is symmetric with respect to the________

Q: Suppose that f is a function defined as f(x) = – 5x + 3x + ¤ + 3. Find an equation for the tangent…

A: Given function is: fx=-5x3+3x2+x+3 We have to find the equation of the tangent line drawn to the…

Q: Let f(x) = -3x° – 3x – 3 | Use the limit definition of the derivative to calculate the derivative of…

A: Here is the solution of the given problem.

Q: Suppose that f(x) = 17ex - exe Find f'(3)= ?

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Q: Sketch a graph of a function ƒ, where ƒ(x) > 0 and ƒ′(x) < 0for all x in (0, 2).

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Suppose that f is a function defined as f(x) = 5x3 + 3x2 + x + 3. Find an equation for the tangent…

A: f(x)=5x3+3x2+x+3Derivative formuladdxxn=n xn-1

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: The domain of f' is 1 (Type your answer in interval notation.)

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Q: Determine from the graph whether the function has any absolute extreme values on [a, b]. Then…

A: For given graph, Absolute Maximum is at x = d. and  Absolute minimum does not exist.

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 f'(x) for f(x) = x³ + x³ . Label at least 3 points on this graph .

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Q: find the domian of the function. verify your result with a graphing calculator table or graph f(x)=…

A: Given function f(x)=x-2x+3

Q: Suppose f is a function with domain [a,b]. If f is an odd function, what can be deduced about a and…

A: According to question f is a function with domain [a, b]  And f is an odd function.

Q: Find f"(x) if f (x)=√√5 - 4x. Show work:

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Q: Sketch a graph of the function f that is continuous on (- 00,00) and has the following properties.…

A: Given, Graph of the function f(x) is continuous on-∞,∞ y=f(x) and has the following…

Q: Sketch a graph of the function f(x) : 2 sin +1 6+ 4 -7 -6 -5 -4 -3 -2 -1 -1 1 2 3 -9 -8 4 5 -2 -3 -4…

A: Given: The function

Q: Find a function f that satisfies the conditions. "(a) --Na (1) - 5, (4) - -1

A: Given Data: The second derivative of the function is: f"x=x-3/2 ......1 The value of the first…

Q: The graph of f' on the interval [-3, 2] is shown below. YA (2, 4) y = f'(x) (-1, 1) (1, 1) 1 (-3,…

A: Graph of f' on the interval -3,2 is given.f'&lt;0 for -3,-2f'&gt;0 for -2,0∪0,2f'=0 at x=-2, x=0.

Q: What conditions have to be checked to determine if a function is "well defined"?  How would I show…

A: Let the function beThen we need to check 3 conditions to prove that the function is Well definedThey…

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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