1) For the function: f (x) = 1+글 + 끓 x² a. Determine the domain, and find HA and VA , and x intercepts. (Horizontal and Vertical Asymptotes) b. Determine Critical numbers, Intervals of Increasing, and Intervals of a Decreasing by using the first derivative test. c. Find IP ( inflection points) and indicate Concavity Change at IP by using the second derivative test. d. Sketch the function.

Q: Given the function g(x) = 4x° + 12x² – 180x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: Find all points (x.y) where f(x.y) has a possible relative maximum or minimum. Then use the second…

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Q: Given the function g(x) = 8x° – 60x + 96x, find the first derivative, g'(x). g'(x) = Notice that…

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Q: Given the function g(x) = 8x³ + 12x² – 48x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

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Q: Given the function g(z) = 6z + 54z² + 90z, find the first derivative, g'(x). %3D = (z),6 Notice that…

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Q: Given the function g(x) = 6z + 63z + 180z, find the first derivative, g´(x). %3D (z),6 Notice that…

A: To Determine: find the first and 2nd derivative also find local maximum and local minimum  Given: we…

Q: Given the function g(x) = 8x – 84x? + 240x, find the first derivative, g'(x). = (x),6 Notice that…

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Q: For the function y= x² -8x +20 a. Determine the critical points  b. Use the sign test to classify…

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Q: Find the local maximum and minimum values of f using both the First and Second Derivative Tests. (If…

A: Differentiate the function fx=xx2+1 with respect to x, to obtain f'(x) and f''(x).…

Q: 1 For f(x) -x² + x + 2, find: a) the equation of the line that is tangent to the graph of f at the…

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Q: 1. Given f(x)= (a) Show that f'(x)= 2(x² -16) 3x by using the quotient rule. Hence, find all 11 the…

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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: Find the critical points of the following function. Use the Second Derivative test to determine (if…

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Q: 8) For the function y = x³ – 9x2 + 24x + 13, use the second derivative tests to: a) determine the…

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Q: Given the function g(x) = 8x* + 84x² + 288x, find the first derivative, g'(x). = (x),6 Notice that…

A: Since, you have ask multiple part's in the question. I am answering for first three parts. Please…

Q: Consider the function f(x) = 52° + 12x – 7. %3D (a) Find the derivative f'(x) and hence the critical…

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Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: Given the function g(x)=8x3-12x2-288x, find the first derivative, g′(x). g′(x)= Notice that g′(x)=0…

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Q: am having trouble finding the equation of the line tangent to the graph of f at (1,1), where f is…

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Q: Given the derivative f'(x), find the x-value for all relative extrema for the graph of the original…

A: Consider the given derivative. f'x=x2−5x+6 Put the first derivative equal to zero.…

Q: Given the function g(x) 6x – 27x2 – 72x, find the first derivative, g'(x). = (x),6 Notice that g'(x)…

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Q: Find the critical point of the function f(x, y) = 7x² + 5y2 – xy + x. Then use the Second Derivative…

A: Relative minima and maxima of function

Q: Use Excel or MATLAB to draw the function v and its first and second derivatives v' and v", for 0 < x…

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Q: Given the function g(x) = 8x° 36x + 48x, find the first derivative, g'(x). g'(x) = Notice that g'(x)…

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Q: Let f(x) = e^(2−x^2). Find the x-coordinates of all critical points of the f. Determine whether each…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

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Q: Given the function g(x) = 4x° – 36x?+ 96x, find the first derivative, g'(x). g'(x) = (x),6 Notice…

A: Given that, the function is g(x) = 4x³ - 36x² + 96x We have to find the g'(x),g"(x) and have to…

Q: Given the function g(x) = 8x + 96x + 360x, find the first derivative, g'(x). %3D = (x),6 %3D Notice…

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Q: Let f(x) = 12 – x2 The slope of the tangent line to the graph of f(x) at - the point ( - 3, 3) is…

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Q: 1.Use the second sufficient condition for an inflection point (the third derivative test) to find…

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Q: Given the function g(x) = 4x° + 30x2 + 48x, find the first derivative, g'(x). gʻ(x) = Notice that…

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Q: Consider a function f with domain {x|x + 0} and the following derivatives: 2 bx3 bx² – 1 bx? f' (x)…

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Q: Given the following function: f(x) = x^2 lnx - Find the critical points for each of the functions…

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Q: 9. Given the function f (x) = 3x -4x2 + 2, use the first and second derivative tests to find: a) the…

A: Since solve the first question for you. If youwant any specific question to be solved then please…

Q: Given the function g(x) = 8x³ + 12x² − 288x, find the first derivative, g'(x). g'(x)= Notice that…

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Q: For each function, perform the following steps: i. Find any critical points ii. use the first…

A: Since you have posted multiple questions, we will solve only first question for you. To getremaining…

Q: B4: a) Find and classify all critical points of the function f(x) = x³ + 3x? – 12x + 5 b) Determine…

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Q: Let f(x) = 33 –x The slope of the tangent line to the graph of f (=) at the point (-5, 8) is The…

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Q: Find the critical points for the following function. Then use the second derivative test to…

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Q: Find the critical numbers of the function f(x) = 14x + |x|. In the answer boxes below, enter the…

A: Given: f(x)=14x3+|x| Definition: Critical points are the points where the derivative of function is…

Q: 3. Consider the function 8x f(x) = + 15. - The tangent line to the graph of f at the point (6, f(6))…

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Q: Find the critical points of the following function. Use the Second Derivative Test to determine (if…

A: The given function is f(x,y)=4x2+2xy2-4x+1

Q: Given the function g(x) 6x + 63x² + 216x, find the first derivative, g'(x). = (x),6 Notice that…

A: We use second derivative test to determine the local Maxima and minima

Q: Given the function g(x) = 8x° + 12x2 – 480x, find the first derivative, g' (x). g'(x) = Notice that…

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Q: 11. (a) Find F'(x) using the limit definition of the derivative if F(x) = F'(x) will result in zero…

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Q: Let f(x) = 21 – x² The slope of the tangent line to the graph of f(x) || at the point (-4, 5) is The…

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Q: Can you help with this problem step by step?

A: (a)

Q: (1) Find the derivative of the function f(x) = 2x³ - 12x² +4 and use it to find the critical numbers…

A: Solution is given below:

Q: Consider the following function. f(x) = x* + 4x3 + 11 (a) Make a sign diagram for the first…

A: We have to find the sign diagram for first derivative,  sign diagram for second derivative,  sketch…

Q: Consider the function h(x) = ((x^2) - x) / ((x + 1)^2), which has first derivative h'(x) = (3x - 1)…

A: To find the vertical asymptotes, locate and classify all relative minima and maxima and point(s) of…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.