VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your answers. 91 Suppose that h() is continuous everywhere, with the graph of h'(x) given on the left. y = h'(x) 1. The function h has a relative minimum at x = 3. (-3,0) (0,-1)] 2. The graph of h is concave down on (0,3). 3. The function h' has an essential discontinu- ity at x = 0. 4. The function h" is decreasing on (-∞, -1). 15 5. There exists c€ (-3,-1) such that h" (c) = -1. (-1,-2) (0, -2) (3,0)

VI. Write TRUE if the statement is correct, otherwise write FALSE. There is no need to justify your answers. 91 Suppose that h() is continuous everywhere, with the graph of h'(x) given on the left. y = h'(x) 1. The function h has a relative minimum at x = 3. (-3,0) (0,-1)] 2. The graph of h is concave down on (0,3). 3. The function h' has an essential discontinu- ity at x = 0. 4. The function h" is decreasing on (-∞, -1). 15 5. There exists c€ (-3,-1) such that h" (c) = -1. (-1,-2) (0, -2) (3,0)

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.
Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it continues on its course indefinitely. Let D(t) denote its distance from Earth after t years of travel. Do you expect that D has a limiting value?
Is there a smooth (continuously differentiable) curve y = ƒ(x) whose length over the interval 0 ≤x ≤ a is always √2a? Give reasons for your answer.
On the graph of f(x)=sinx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?
What value of a makes ƒ(x) = x2 + (a/x) have a. a local minimum at x = 2? b. a point of inflection at x = 1?
Find the absolute extrema of the function h(x) = ex2 − 4 on [−2, 2] Absolute maximum value: at x = ± Absolute minimum value: at x =
A manufacturing company owns a major piece of equip -ment that depreciates at the (continuous) rate f= f(t) ,where is the time measured in months since its last overhaul.Because a fixed cost is incurred each time themachine is overhauled, the company wants to determine theoptimal time T (in months) between overhauls.(a) Explain why ∫0t f(s) ds represents the loss in value ofthe machine over the period of time t since the lastoverhaul. (b) Let C =C(t) be given by C(t) =1/t[A + ∫0t f(s) ds]What does C represent and why would the companywant to minimize C ?(c) Show that has a minimum value at the numbers t =Twhere C(T) =f(T).