) Graph the following functions: V4 - x2 ,-2

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

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Q: 1) Find the absolute extremum values of f(x) = x² - 3x + 12 over the interval 1, 3]. -

A: The extreme value of function at f(3)= 30

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

A: Given   y = sin (x3) ....(1)   , (1, 2)

Q: тт Find the absolute minimum and maximum of f(x) = 2 sec x tan x on the interval [-- 4' 4

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Q: Sketch a graph of the function f(x) 2 sin(2x). %3D -77/8-31/4-5n/8-/2 -3/8-7/4-T/8 t/4 3n/8- /25/8…

A: Given function is f(x)=-2sin(2x)We know that period of sin(x)=2πThe period of sin(2x) will be π and…

Q: 1. Find the absolute extrema. 1) f(x) = 5 – x² on [-5,4]

A: fx=5-x2,  -5, 4 Differentiating with respect to x, we get f/x=0-2x=-2x Now to find critical numbers,…

Q: Find the absolute maximum and minimum values of the function f(x)-cos²x-3sinx on the interval 0≤x≤7.

A: First I have find the derivative of the given function and set them to zero .Solved them to get the…

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: ,x5 (A) 5 (B -4 6 3 (E) none of the given choices

A: Given that, The function f(x) is following, f(x)=x-4,x≤5kx2-24x+46,x>5 We have to find the value…

Q: c) lim,→1+ f(x) where f(x) = { V1- x, x 1 | x +1,

A: Given query is to find indicated limits.

Q: 7. Is the function given by G(x) at x = 2? Why or why not? 1 x² - 6x + 8 continuous

A: Theory : If A function f(x) is continuous at some point a, then it must satisfy All of these…

Q: . How many point(s) of inflection are on che graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x² -…

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Q: * Graph f(x) = 3 sin (x) on the interval [0,4]. Be sure to laber maximum, minimum, and x intercepts.…

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Q: (1 point) Suppose f" (x) = –16 sin(4æ) and f' (0) = –4, and f(0) = -1. -1. f(T/2) :

A: Given,f''x = -16sin4xIntegrating on both side with respect to x, we get;f'x = - 64cos4x +…

Q: On the graph of f(x)=cosx and the interval [2π,4π), for what value of x does f(x) achieve a maximum?…

A: see attached file for a detailed solution.

Q: At what points is the function is continuous y=|2x-1| +4sin(2x)

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

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Q: If an odd function f(x) has a local maximum value at X=c which of the following must be true?

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Q: Sketch a graph of the function f(x) = 0.5 sin(3x). 4+ 2 -5/6 -27/3 -T/2 -T/3 -Tt/6 T/2 2/3 5/6 -1 -2…

A: Here is the solution

Q: when x # 1 Show that f(x)% = 2 when x =1 is discontinuous at x 1

A: Given query is to find the continuity of the function at x = 1.

Q: Find the absolute maximum and minimum values of ƒ(x) = ex - 2x on [0, 1] .

A: Consider the given function.

Q: ,for x 1 Discuss the contuniuty of f andf'.

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Q: 1 Sketch a graph of the function f(x) = 3 sin 5- 4- -87T -7 -6I -5 -47T -37 -27 27T 37T 47T -2- -3…

A: the amplitude of the function is 3 the time period of the function is  2π1/4=8π

Q: Find the value of k that makes function continuous at z = 4 | 2x + 8 x> 4 4x k x < 4 f(x) =

A: If the function is continuous at x=4 then the left and right-hand limit at x=4 should match. That…

Q: Suppose f''(x) = -(sin(x)), f'(0)=6 and f(0)= -1 Find f(π/2) =?

A: Given query is to find the value of the function at indicated point.

Q: 10. Find a function f such that f'(x) =r' and the line 4x - ļy = 3 is tangent to the graph of f. %3D

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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: Sketch a graph of the function f(x) = 3 sin(3x). 4 -5/6 -2/3 -/2 -T/3 T/2 2t/3 5t/6 -1 -2 -3 3. 2.

A: Sketch a graph of the function  f(x) = -3sin(3x)

Q: Find for the following function: 1- y = etan'x 2-x'y+ x*y 2 at x = 2

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Q: Find a function y whose graph passes through the point (1, =) and satisfies x2y' = y.

A: NOTE: Refresh your page if you can't see any equations. .

Q: At which point does f(x)=2sinx-cos the maximum value over the interval [0.2 * pi]? 2x have an…

A: f(x)=2sin(x)-cos2(x) f'(x)=2cos(x)+2sin2(x) Now to find the critical number, f'(x)=0

Q: If f(x) = etan-¹(x²) then f'(x) at x = 1 is equal to TU 2e4

A: The explanation of answer as follows :

Q: 3. Find the absolute maximum and the absolute minimum of f(x) = x-2 tanx on the interval [0,4].

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Q: 5. Let f(x)= x . arccos x. Find f'(-/3/2) ||

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Q: Use the Intermediate Value Theorem to show that the graph of f(x) = 4tan(x) – x + 1 intersects the…

A: Please note that according to guidelines only first Q is solved. Please repost the other question.

Q: 1. How many point(s) of inflection are on the graph of f(x)=18x^3+5x^2-12x-17 * f(x) = 18x + 5x2 -…

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Q: If f (x) = 3 sin x + 7 and g(x) = 2x – 7, what is the maximum value of f(g(x))?

A: Here given that                          f(x)=3sinx+7             and      g(x)=2x-7 We have to find…

Q: 12. The graph on the right is NOT differentiable at x = 1. For what reason is it not differentiable?

A: Yes, given graph is correct.Given function:f(x) = x-1f(x) = -x+1        x&lt;1x-1           x≥1

Q: If 7x-5,x < 1 h(x) 3x2 – x, 1 < x < 3 Is h(x) continuous at (x=1)?

A: Given: hx=7x-5,x&lt;13x2-x,1&lt;x≤3 We know that any given functiony=fx will be continuous at x=a…

Q: 4. Find the point on the graph of f(x) 5x + 20x – 3 where the tan gent line is horizontal. 5

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

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Q: 1 - X 0 3

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Q: 1. Find all the local and global extrema of the function f (x) = sin(x) – x [-27, 27]. Clearly…

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Q: 4. If f(x) = sin x, show that f(2.x) = 2f(x)f(-x) %3D

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Q: Find points of discontunity of the function,where k is real number 1 f(x, y) sin(4 – x2 – y?) - -

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Q: 2. Consider the function а(т — 2) Vx +2 – 2 - if x 2, 2x 2 x² - where a, b, c are real numbers.…

A: Given function is  f(x)=a(x-2)x+2-2   if x&lt;2b                     if x=21x-2-cx2-2x  if x&gt;2…

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

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Q: 7, The inflection points of the function f(x)%= 글어 -금 + 12-음 ocurs at OCcurs at: ||

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Q: There is an infinite discontinuity at x = 0 and f(0)=-2

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.