a. Determine whether the Mean Value Theorem applies to the function f(x) = -4+x on the interval [-1,2].b. If so, find the point(s) that are guaranteed to exist by the Mean Value Theorem.a. Choose the correct answer below.O A. No, because the function is not continuous on the interval [-1,21, and is not differentiable on the interval (-1,2)O B. No, because the function is differentiable on the interval (-1,2), but is not continuous on the interval -1.21OC. No, because the function is continuous on the interval -1,2, but is not differentiable on the interval (-1.2)O D. Yes, because the function is continuous on the interval -1,2] and differentiable on the interval (-1.2)b. Select the correct choice below and, if necessary, fill in the answer box to complete your choiceO A. The point(s) is/are x=(Simplify your answer. Use a oomma to separate answers as needed)B. The Mean Value Theorem does not apply in this case.

Answered: Image /qna-images/answer/f318730a-b063-4025-9dbd-a697a277edb1.jpg

Answered: continuous on the interval [-1,2), and…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The logistic function given by f (x) 1 is a sigmoid (s-shaped) function useful in many 1+e-* areas of mathematics and computer science. The function f is a bijection, whose domain is R and range is (0, 1). (a) function g : (0, 1) → (a, b), show that |R| = |(a, b)|. Given an arbitrary interval (a, b), by using the composition of f with an appropriate (b) By using part (a) show that [a, b] = (a, b). (c) The derivative of f is equal to f'(x) = f(x)f(-x). Show that f' is not one-to-one.
Suppose we were asked the question: "A rectangle is to be inscribed in a circle of radius 5cm. What is the width of the largest (biggest area) such rectangle?" Let A(w) denote the corresponding area function in terms of the width of the rectangle. At which type of point will the answer occur?
good notation and show all of your work 1. Graph the function where: (a) Continuous and differentiable for all real numbers (b) f'(x) >0 on (-00,-3) U (1,4) (c) f'(x) 0 on (-1,2) (f) f'(-3) = f'(4) = 0 (g) f"(x)=0 at (-1,3) and (2,4) Graph the function where: (a) Continuous for all real numbers (b) Differentiable everywhere except at x=4 (c) f(1) = 5 (d) f'(1) = 0 and f'(3) = 0 (e) f'(x) > 0 on (-∞, 1) U (4,0) (f) f'(x) 0 on (2,3) (i) f"(x) <0 on (-∞, 2)U(3, 4)U(4,00)
Let g(x)=V 64x2 - 4 The function g is increasing on the following interval(s): (-∞, ∞) (-00, a) (-0, a] O (a, o) O [a, 0) (-∞, a) U (b, ∞) O (-∞, a] U [b, ) O (a, b) (а, b] [a, b) O [a, b] None a = 1/4 b = DNE g is decreasing on the following interval(s): O (-∞, ∞) (-0, c) O (-∞, c] O(c, ) O[C, ) O(-, c) U (d, 0) 0(-∞, c] U [d, ) (c, d) O(c, d]
Suppose for a function h where its domain is R-{-2,2} We know that h'(0) = 0 y h(0) = 2 ▪h'(x) > 0 si x € ]0,2[ 0 x € ]2, +∞[ ▪h'(x) < 0 si x € ] -2,0[ ox]-∞, -2[ Consider the statements 1- In the interval ]2, +∞o[ is decreasing 2- It has maximum relative at (0,2) Which are true? A) both B) None C) Just 1 D) Just 2

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