3 x>2 12 Sketch the graph of f:R→R f (x)={2x-1 -1sxS2 -2 x<-1 At what points is the graph continuous?

Q: A function f(t)= 5x + 8x^-1 has one local minimum and one local maximum what is the function has a…

A: Given query is to find the local maximum and the minimum for the function f(x).

Q: c) Use Secant Method to find the root of f(x)= x -x-1 with two initial points x, = 1 and=1.5 and =…

A: Secant method Steps  Step-1: Find points x0 and x1 such that x0&lt;x1 and f(x0)⋅f(x1)&lt;0.…

Q: 5) f(x) = x³ – x² + 1 B) Removable discontinuity at: x =-1 Essential discontinuity at: x = 1 A)…

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: 4. Sketch the graph of a continuous function g for which all the following are true.: 8 (5) = 3, g…

A:

Q: Find the local and/or absolute maxima for the functions of the specified domain. Y= 1/(x-x^2) over…

A: Here we have to use the concept of derivatives. Here we use second derivatives test for finding…

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

A:

Q: 5. Find the absolute extrema of f(x) = x’ + 3x – 9x + 4 on the closed interval [-4, 0].

A: The given function fx=x3+3x2-9x+4

Q: (mx²- -3x+1 f(x) = x + 1 of function x=1 continuous at the х-1 X = 1 point of What should m and n be…

A: The given function is, f(x)=mx2-3x+1x-1,x≠1f(x)=n,x=1. That is,…

Q: ,x 1 Is the function k(x) = {x²-1 2,x = 1 continuous at x = 1?

A: We use L' hospital rule to find the limit.

Q: Find the maximum and minimum values of the function y = 4V x2 + 1 - x on the interval [0, 2]. (Round…

A:

Q: The absolute maximum of f(x) = 3 x3 -2x On [-1,8] is y= OA 0. OB 5 OD A-

A: For Maximum value of f we need to get the respective value of x by differentiating the function and…

Q: 7 Sketch the graphs of f (x) = sin(π x) and its dilates f (3x) and 3f (x)

A: f(x)=sin(πx)

Q: Find the absolute maximum and absolute minimum values of f on the given interval. (If an answer does…

A:

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: 11.  Let h(x) = x^4 − 2x^2 + 3.(a) Find all critical points and use the First Derivative Test to…

A: Given information:The given function is shown below:

Q: -2 Find the interval(s) where f(x) =- 64-x2 is continuous.

A:

Q: I. Is the function given by g(x)=x²-3x + 2 continuous over the interval (-4, 4)? Why or why not?

A: Function given is- g(x)=x2-3x+2 continuous over the interval (-4,4) . Wee need to determine whether…

Q: Q1- Find any local maximum and local minimum values and sketch the curve: x? + 1 f(x) = x2. - 1

A: Given that  f(x)=(x^2+1)/(x^2-1) To find the local maximum and local minimum

Q: 2. f(x) = is a continuous function but it is discontinuous at x = 3. Explain why X - 3 this is not a…

A:

Q: Give an example that: the function f has a local maximum at x = 1/2, but it is not differen- tiable…

A: Consider the function:

Q: Find the exact location of all the relative and absolute extrema of the function. f(x) = 2x - 2…

A:

Q: 1. Find the absolute extrema of f (x) = x* - 8x² + 3 on the interval [-1,3].

A: Absolute extrema on a closed interval lies on end points or at f'(x) = 0 So first we have to…

Q: 3. Sketch the graph of a function that is continuous, but not differentiable at I= 1.

A:

Q: sketch the graph of each function and determine whether the function has any absolute extreme values…

A:

Q: 10. At what value of 'x' does a local maximum of y= x^3 - 3x occur?

A: We will solve the following

Q: 8. Find the absolute extrema of f(x) = 6x + 4 + on the closed interval [1, 6].

A: Given : The function is f(x) = 6x + 4 +24x and the closed interval [ 1, 6 ].

Q: FIND a) F(5) b)interval over which F(x) is decreasing  c) what x=? Where F(x) has a maximum value

A: Given, F(x)=∫0xf(t)dt Graph,

Q: 7) Find the absolute maximum of the function f on (0,0) f(x) =10xe2* %3D

A:

Q: 111. Consider the piecewise-defined function f defined by: x2 + 2, for -25xs 0, for 0 <x< 4, for 4…

A: Solution:Given   f(x)=x2+2-2≤x≤020&lt;x&lt;4x-24≤x≤6To find:(a) sketch the graph(b)Identify the…

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: Determine the maximum number of turning points of f. 6. f(x) = (x – 2)2(x + 4)2 7. Identify the end…

A:

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

A:

Q: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)&lt;0 and f(1)&gt;0  f(x) is a continuous function.

Q: 6. Find the absolute extrema of the function f (x) = 7x² + 1 on the closed interval [-1,2].

A: We need to check value of f(x) on critical points and boundary values of interval to find absolute…

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

A:

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: 7. Find the absolute maximum and minimum of f(x) = x!/² ( on the interval [0, 4]. %3D

A:

Q: 1. Give an example of a function f : R –→ R that is continuous and bounded but does not achieve…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 17 The function f is defined by f(x) = 5x - c, where c is a constant. In the xy-plane, the graph of…

A: Solve both the problem in the following way:- (i) given point will satisfy the function. (ii)…

Q: Find the absolute maximum and absolute minimum values of the function f(x) = 2x – 15 In(7x) on the…

A:

Q: f(x) = xln(2x) find the f '(0.5) as well as f''(1) and where is the absolute minimum located/ where…

A: This question is based on maxima and minima of function .

Q: 2 The function f(x)= (x² – 1) ³ , is decreasing on the interval (- 00,-2)U (0,2) AO (-1,0) U (1, ∞ )…

A:

Q: Find the absolute maximum and absolute minimum values of the function f(æ) = 2x – 15 In(3x) on the…

A:

Q: A function y = f(x) is decreasing on the interval [0, 5]. What conclusions can you draw about the…

A: A function is increasing, if when x increases, the value of y also increases.          Since the…

Q: 4. Sketch a continuous curve y = f (x) with the stated properties. g(3) = 2, g'(3) = – g"(x) > 0 for…

A: Given query is to find the graph of the function according to the properties given.

Q: Find the x value where the function g(x) = xe-lx attains a local maximum. Enter the exact answer. If…

A: Differentiate y and by solving y'=0 obtain critical points. Check sign of y'' on critical points -…

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

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Q. 1: Determine the func- tion is continuous or dis- continuous at x = -1 and x = 1.

A:

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…

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.