39–48. First Derivative Test a. Locate the critical points of f. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). 39. f(x) = x² + 3 on [-3, 2] 40. f(x) = -x² – x + 2 on [-4, 4] %3D 41. f(x) = xV4 – x² on [-2, 2] 42. f(x) = 2x³ + 3x² – 12x + 1 on [-2, 4] 43. f(x) = -x³ + 9x on [-4, 3] %3D 44. f(x) = 2x5 – 5x4 – 10x3 + 4 on [-2, 4] %3D 45. f(x) = x2/3 (x – 5) on [-5, 5] x2 46. f(x) = 2 on [-4, 4] x² – 1 47. f(x) = VīlIn x on (0, *) 48. f(x) = tan x - r' on [-1, 11

39–48. First Derivative Test a. Locate the critical points of f. b. Use the First Derivative Test to locate the local maximum and minimum values. c. Identify the absolute maximum and minimum values of the function on the given interval (when they exist). 39. f(x) = x² + 3 on [-3, 2] 40. f(x) = -x² – x + 2 on [-4, 4] %3D 41. f(x) = xV4 – x² on [-2, 2] 42. f(x) = 2x³ + 3x² – 12x + 1 on [-2, 4] 43. f(x) = -x³ + 9x on [-4, 3] %3D 44. f(x) = 2x5 – 5x4 – 10x3 + 4 on [-2, 4] %3D 45. f(x) = x2/3 (x – 5) on [-5, 5] x2 46. f(x) = 2 on [-4, 4] x² – 1 47. f(x) = VīlIn x on (0, *) 48. f(x) = tan x - r' on [-1, 11

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter1: Functions

Section1.2: Functions Given By Tables

Problem 32SBE: Does a Limiting Value Occur? A rocket ship is flying away from Earth at a constant velocity, and it...

See similar textbooks

Similar questions

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?
The oxygen supply, S, in the blood depends on the hematocrit, H, the percentage of red blood cells in the blood. If S = k(H) = aHe-bH for positive constants a and b, with domain (0, infinity) and k'(H) = ae-bH(1-bH) 1. Use the definition to find the only critical point H1 of k on its domain. 2. Use a number line and the first derivative test to show that the oxygen supply is maximised at H1.You have to explain how you determine the sign of the first derivative on every interval. 3. What is the maximum oxygen supply? 4. How does increasing the value of the constants a and b in the same proportion change the maximumvalue of S? Please answer 3 and 4
3. The function f(x) = x^4 − 4x^3 + 8x has a critical point at x = 1.(a) Find f"(x). (b) Then use the second derivative test to identify the critical point as eithera local minimum, a local maximum, or neither.
A-Find the local minimum and maximum of f(x)=xe^3x using the first and second derivative test. B-Find the value of a so that the function f (x) = xeax has a critical point at x = 3.
a) On the number line, mark the critical value(s) of f(x) and the sign of the first derivative between them as obtained from the graph. b) Where is f(x) increasing on it's domain? c) Where is f(x) decresing on it's domain? e) At what x-value(s) would f(x) have a relative maximum? d) At what x-value(s) would f(x) have a relative minimum?
1) Use the First Derivative Test to determine whether the function attains a local minimum or local maximum (or neither) at the given critical point y=x2/x+1, c=0 1a) find the critical points and the intervals on which the function is increasing or decreasing, and apply the First Derivative Test to each critical point y=x5/2-x2 (x>0)
1. A critical number of f′(x) is an inflection point of f(x).True or False 2. If the radius of a circle is increasing at a constant rate, then so is the circumference.True or False 3. If two variables x and y are functions of t and are related by the equationy = 1 −x^2, then dy/dt = −2x.True or False 4. When finding the global minimum of a function on an interval, you must usethe first or second derivative test to verify that your point is a global minimum.True or False
Find the X coordinates of all critical points of the given function. Determine whether each critical point is a relative maximum, relative minimum, or neither by first applying the second derivative test, and, if the test fails, by some other method. g(x)=3x^3-9x+9 (a) g has a relative maximum at the critical point X=_____(smaller x value) (b) g has a relative minimum at the critical point X=_____(larger x value)
Find the minimum and maximum value of the function on the given interval by comparing values at the critical points and endpoints:y = 5 tan−1 x − x, [1, 5]
2. f(x) = x^3 − 27x (a) Use the derivative of the function f(x) to find all critical points. (b) Draw and use a graph to classify each critical point of f(x) as a local minimum, local maximum, or neither.
find the minimum and maximum value of the function on. the given interval by comparing values at the critical points and endpoints.y ] =√2 θ − sec θ,[0, π/3]
find the minimum and maximum value of the function on. the given interval by comparing values at the critical points and endpoints. y = 3ex − e2x , [-1/2,1]