Consider the graph of the function f(x) = (x^2 - 2x + 4) / (x - 2) , in the interval O < x < 2, the f(x) is increasing and concave downward O decreasing and concave downward O increasing and concave upward decreasing and concave upward O NA

Q: Let f(x)=x² -3x+5. Show that the average rate of change of f (with respect to x) on an arbitrary…

A: Average rate of change = (f(b)-f(a))/(b-a) Instantaneous rate of change =f'(a+b/2)

Q: 1 f(x) rank- 3x

A: Let's find.

Q: For the function, f(x) = 9x² – x³ - a. Use the derivative to find all critical points b. Classify…

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Q: Find max and min of function on the interval    f(x)=-x4-x3+5x2-4 on [-2,1]

A: The given function is; f(x)=-x4-x3+5x2-4 on [-2,1]

Q: Find the absolute minimum and absolute maximum values of f on the f(x) = In(x2 + 3x + 8), [-2, 2]…

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Q: Find local maximum or local minimum of f(x)= -sin 2x -x defined on 22

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Q: Suppose we know that f(x) is continuous and differentiable on the interval [-8, 0], that f(-8) = -9,…

A: Given data: The value of function is, f(-8)=-9 The value of differentiating function  f(x)≤2

Q: Find the absolute extrema of the function on the closed interval. f(x) = 7 – x, - [-4, 4] minimum…

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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&lt;5x+1            ,  x≥5

Q: Use second derivative test, If x3 f(x) = 25x + 5 then f(x) has a 3 local maximum at the point x = -3…

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Q: Give an example of a function that is continuous but differentiable at x=2

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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: Find f'(x). 6. f(x) = 4x + 7x f'(x) = Compare the graphs of f and f' and use them to explain why…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. g(x) = x +-,4]

A: here we need to find absolute maximum and absolute minimum values of given function . the solution…

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   To find : f'(x)

Q: Sketch the graph of a function on the interval [3,9] that has an absolute maximum at x=5 and an…

A: Ques:-   Sketch the graph of a function on the            intervel 3,9 that has as absolute…

Q: Find the absolute extrema of the function on the closed interval.                      g(x) = 6x2/(x…

A: Given    g(x)=6x2x-2 ;  -2,1

Q: Sketch the graph of the floor function f(x) = x+ 1| over the interval [-3, 3) %3D Show your work

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Q: 3. Find all -values where the graph of f(x) = x³ + 3x² + x + 3 has a horizontal tangent line.

A: Solution is given below:

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: For the function f(x) = 2x4 - 16x2 , find and identify any extrema (maximum/minimum) using the…

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Q: What is the relationship between functions whose limits can be obtained by direct substitution and…

A: We need to define the relation between a limit and continuous function.

Q: Find the exact location of all the relative and absolute extrema of the function: f(x) = 5x^3 − 60x…

A: Given function f(x) Differentiate the function and make it equal to zero for critical points

Q: 3. Is the function given by (x²-4x-5, x<5 F(x)= x+1, x25 continuous at x = 52 why or why not ?

A: Given function, f(x)=x2-4x-5;x-5;x&lt;5x+1;x≥5; The objective is to tell whether the function is…

Q: What is the maximum point of the function f (x) = x² - x on the o terval [-2,2]?

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Q: How would you define f(2) in order to make f continuous at 2? limx→2 x^3-8/x^2-4 show ALL of your…

A: Let's solve limit problem.

Q: Is the function 1 >-{ f(x) = √x x3 x < 0 0 ≤ x ≤ 1 piecewise continuous or piecewise smooth on [-1,…

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

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Q: 2. Use the second derivative test to determine the local minimum and maximum points of the graph of…

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Q: Verify Mean value theorem for the function f(x)=4x^3 over the interval  [0, 2].

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Q: Find the absolute minimum and absolute maximum values of f on the given interval f(x) = x - In(2x),…

A: see next step

Q: Find local maximum or local minimum of f (x)=sin 2x-x defined on 2 2

A: The given function is fx=sin 2x-x. Obtain the critical points as follows. Find f'x as…

Q: Find the maximum and minimum values of the function y = V8 + x2 - 4x on the interval 3, 5|. (Use…

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Q: 5. Use the second derivative test to determine whether f (x) = x3 – 9x2 + 24x +5 has a local maximum…

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Q: Graph the function y =x + 1                                      x2+1 by applying the first and…

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Q: Find the specific that h (-3) =7 function satisfies hlx)こ 6-5x+x and

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Q: Find a formula for a function that has vertical asymptotes x = 6 and x = 8 and horizontal asymptote…

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Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: Find the x-coordinate of the absolute maximum and absolute minimum for the function…

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Q: How should the function f(x)=x²-25/x+5 be defined at -5 to make it continuous at -5?

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Q: Sketch the graph of an increasing function such that f'' (x) changes from + to − at x = 2 and from −…

A: Sketch the graph of an increasing function such that f”(x) changes from + to - at x = 2 as follows.

Q: Find f'(x). f(x) = e – x³ arctan(x) -(3 + 3x2 arctan(x) + arctan(x)(3x4)) x2 +1 f'(x)

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Q: Use the second derivative test to locate all local extrema for the function f(x)=x3−32x2−18x. At…

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Q: Investigate the connections between key properties such as increasing/decreasing intervals, local…

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Q: f(x)=√√x at x = 7

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Q: Find the absolute maximum value of f(x)=(x)(x-1)(x+1) on the interval [-1,1].

A: Definition used -   Absolute maximum value of function - First we equate the first derivative of…

Q: Use the First Derivative Test to find the x-value(s) at which the function 4 f(x) = x4 - 4x² + 1 X.…

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Q: By the definition show that f(x) = 2 + |x| is a continuous graph at the origin. Also, show the…

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