2.Produce graphs of f that reveal all the important aspects of the curve. Then use calculus to find the intervals of increase and decrease and the intervals of concavity. (Enter your answers in interval notation. Do not round your answers.) f(x) = (1/x^12)-(2x10^6/x^6) 2a)find the interval of increase and decrease 2b)find the interval where the function is concave up and concave down

Q: 7. Use calculus to find the exact values of the x-coordinates of all points of the graph of f(x) =…

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Q: Determine the points at which the function is not analytic: (3z - 1) / (z^2 + z + 5)

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Q: Find the absolute extrema of the function on the closed interval.                         f(x) = 2x3…

A: We find the critical points by solving f'(x)=0 -1 is not in the interval [0,3] 1 lies in [0,3]

Q: 2. Graph the function f (x)= x+ Vlx\ . Zoom in repeatedly, first toward the point (-1, 0) and then…

A: Note: There are multiple questions. No specific question has been asked.So, We will solve the first…

Q: Find the point of inflection of the graph of the function. (If an answer does not exist, enter DNE.)…

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Q: Find the intervals of concavity and any inflection points for the function f(x) = -x²e".

A: Given query is to find interval of conavio amd inflection points.

Q: 2. Neatly sketch an accurate graph of the function f(x) = (x + 4)(x + 1))(x – 3). Clearly label all…

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Q: 1 is discontinuous. Find the distance between the two values of x at which the function x² -3x + 2

A: Given rational function is as below

Q: Determine the open intervals on which the graph of the function is concave upward or concave…

A: Solution:Given     f(x)=x2+1x2-1To determine the open interval on which the graph of the functionis…

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

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Q: 24: Find the extreme points of the function f(x) = x + y ху On the circle x+y=2

A: We shall find out extreme points of the function in the next using the a equation of circle.

Q: Determine the intervals of concavity and inflection point(s) for the function f (x) = 3x – 5x“ – 1 -

A: The given function is f(x)=3x5-5x4-1

Q: When a function is discontinuous at x=2, does that necessarily mean that 2 is not in the domain of…

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Q: Find the absolute extrema of the function on the closed interval.                          f(x) =…

A: The given function is Solve the absolute extrema on closed interval [0,4] by finding its derivative…

Q: 3 Determine the intervals for which the function f(x) = x° + 18x +2, is decreasing.

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Q: Explain why the function is discontinuous at the givennumber a . Sketch the graph of the function.

A: fx=1-x2    if  x<11x       if  x≥1 To check the continuity at a = 1. we find the left hand and…

Q: Use the graph of the function to estimate the interval on which the function is decreasing y Enter…

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Q: 7) Determine the intervals where the graph of function is concave upward or concave downward and…

A: Given: f(x)=x3-3x2-9x+1 To find: The interval where the graph of the function is concave upward or…

Q: Find the absolute extrema of the function on the closed interval.

A: Relative extremum of a function are critical points of the function. Critical points of a function…

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 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: f(x) = x – !

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Q: Let  f(x) = x3 − 5x2.  Find the points on the graph of f where the tangent line is horizontal.…

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Q: 3) If a function is continuaus at x=a, then it is differentiaoe at x-a, yes? or NO? why ?

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Q: Find the points on the graph of f(x) = 2x3 + 15x2 - 84x + 12 where the tangent is horizontal. List…

A: we have to find the points on the graph of the function f(x) = 2x3 + 15x2 - 84x + 12 where the…

Q: Find the x-coordinates of all points where the graph of f(x) = 2x^3+9x^2-168x+21 has a horizontal…

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Q: Sketch the graph of f(x) by hand and use your sketch to find the absolute and local maximum and…

A: Graph of f(x) is as follows :

Q: Find the absolute extrema of the function on the closed interval.                        f(x) = 7x2…

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Q: Let f(x) = x³ – 8x². Find the points on the graph of f where the tangent line is horizontal. (Enter…

A: Given data:   The given equaion of the curve is f(x)=x3-8x2.   When the tangent line is horizontal…

Q: Use Intermediate Vaule Tun to show that the functions f(x) = x^3 and g(x) = 2x + 3 intersect at at…

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Q: Find the points of inflection and discuss the concavity of the graph of the function f(x)= x +…

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Q: III. Verify if the function is continous at the point. 1. f(x) = x³ – 2x² + x – 5 at x = 0

A: f(x) is continuous at x=0 if- limx→0-f(x)=limx→0+f(x)=f(0)

Q: and g:y → X. If gof -Ix => Show that f is one-to-one function %3D and 8 is surjective function ?

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Q: Find the absolute extrema of the function on the closed interval.                        f(x) = x3 −…

A: Given the function f(x) = x3 − 3/2x2 We need to find the absolute extrema of the function on the…

Q: Explain why the function is discontinuous at the givennumber a . Sketch the graph of the function.

A: The function is given , fx=x2-xx2-1 ,  if x≠11,     if x=1 for a=1. To check the function…

Q: 14. Use the curve sketching procedure to analyze the function. a. y-x'+x*-20x

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Q: 11. Sketch the graph of the following function. f(x)= x³ - 6x² - 9x [1]x- and y-intercepts

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Q: 16. Sketch the graph of f(x)=(4-x)(x+1)(x+3)*. Be sure to label all x- and y-intercepts.

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Q: Sketch the graph of f by hand and use your sketch to find the absolute maximum and minimum values of…

A: The graph of the function is given as below:

Q: 11. Sketch the graph of the following function. f(x)= x³6x² - 9x [1]x- and y-intercepts

A:

Q: function

A: We are given a function : f(x)=x2-2x+2x-3 We have to determine the domain of given function where…

Q: Find the numbers at which the function is given   is discontinuous. At which of these points is f…

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Q: 46. Let f(x) = x³ - 4x² . Find the points on the graph of f where the tangent %3D line is…

A: 46. The given function is fx=x3-4x2. Differentiate fx with respect to x. f'x=ddxx3-4x2=3x2-8x Now,…

Q: Find the absolute extrema of the function on the closed interval. f(x) = x3 - 12x, [0,6]

A:

Q: . Find the length of the graph of the function f (x) =x* + x2 -<x < 3. on the ir

A: The length of the graph of y=f(x) from x=a to x=b is given by:∫ab1+f'(x)2dx f'(x):…

Q: Find the horizontal and vertical asymptotic for f(x)= 1/(1-x^2)

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Q: At the point x = 2, the function J x-2 -< rs2 -8 2<x< f(x) = is (a) continuous and differentiable…

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. 3 -4 -2…

A: According to company policy we are allowed to provide solution for only first 3 sub parts. If you…

Q: Find the open intervals on which the function is increasing or decreasing.       y = x√(16 − x2)

A: The given function is , y=x16-x2

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.