TRUE OR FALSE. Determine if each statement is true or false. 1. If fis differentiable on [-1,1] then fis continuous at x=0. 2. All critical points of f(x) satisfy f(x)=0. 3. It is possible that functions f and g are not continuous at a point xp, but f+g is continuous at xg.

TRUE OR FALSE. Determine if each statement is true or false. 1. If fis differentiable on [-1,1] then fis continuous at x=0. 2. All critical points of f(x) satisfy f(x)=0. 3. It is possible that functions f and g are not continuous at a point xp, but f+g is continuous at xg.

Name: #8 (1-3) TRUE OR FALSE. Determine if eachstatement is true or false.1.
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: #8 (1-3) TRUE OR FALSE. Determine if eachstatement is true or false.1. If fis differentiable on [-1,1] then fiscontinuous at x=0.2. All critical points of f(x) satisfy f(x)=0.3. It is possible thatfunctions fand g are not continuous at apoint xp, but

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter3: Functions

Section3.3: More On Functions; Piecewise-defined Functions

Problem 99E: Determine if the statemment is true or false. If the statement is false, then correct it and make it...

See similar textbooks

Similar questions

Determine if the statemment is true or false. If the statement is false, then correct it and make it true. If the function f increases on the interval -,x1 and decreases on the interval x1,, then fx1 is a local minimum value.
1. Consider the following Pieces wise function: F(x)={ 4x/(x^2+1) −4 ≤ x ≤ 0 {-x/(4x^2+1) 0<x≤2 (a) Is f(x) continuous at x = 0? Explain why. Show work (b) Is f(x) differentiable at x = 0? Explain why. Show work (c) Find all the critical points of f(x).Show work (d) Find the (absolute) maximum and minimum of f(x). Show work
Generate a continous and differentiable functiin f(x) with the following properties: f(x) is decreasing at x=-6, f(x) has a local minimum at x= -3, f(x) has a maximum at x= 3
Given a continuous function f with exactly one critical point.Find the x-values at which the local and global extremes occur iff'(2) is undefined, f'(x)=-1 for x<2, f(1)<f(4) and f'(x)=1 for x>2 on [1,4]
What are the maximum and minimum values of the function y = | x | on the interval -1 ≤ x < 1? Notice that the interval is not closed. Is this consistent with the Extreme Value Theorem for continuous functions? Why?
Find a constant b such that h is continuous at x = 2, where h(x) = {x + 1 for lxl < 2 b - x 2 for Ix I > 2 With this choice of b, find all points of discontinuity.
Explain the Answer of the following question: Aside from Extreme Value Theorem (EVT), there is another theorem behind optimization, the Fermat’s Theorem: Let ? be a continuous function on an open interval ? where ? is in ?. If ? has an extremum at ?, then ? must be a critical number of ?. Expound this theorem.
2. Suppose that f(x) is a function continuous for every value of x whose first derivative is f'(x) = 2(1-x^2)/1+x^2 and f"(x)= 4x(x^2-3)/ (1+x^2)^2 Further, assume that it is known that f has a horizontal asymptote at y = 0. and a. Determine all critical points of f. b. Find the intervals on which the graph of f is increasing or decreasing.
Suppose f is continuous on an interval containing a critical point c and f 1c2 = 0. How do you determine whether f has a local extreme value at x = c?
Let g be a function such that g'(x) = x (x - 3). Complete the following arguments to get all relative extrema from the Second Derivative Test: The critical number(s) of g where g'(x) = 0 is/are [ both 0 and 3, neither 0 and 3, 3 only, 0 only ]? After computing g'', we find that g''(0) is [ Undefined, Postive, Negative, Zero ] ? and g''(3) is [ Undefined, Postive, Negative, Zero ] ? Therefore: [ f has a local minimum, We cannot conclude from the Second Derivative Test, f has local maximum ] at x = 0. [ f has a local minimum, We cannot conclude from the Second Derivative Test, f has local maximum ] at x = 3.