#40 part c Applying the First Derivative Test In Exercises 21-56,(a) find the critical numbers of f (if any), (b) find the openinterval(s) on which the function is increasing or decreasing,(c) apply the First Derivative Test to identify all relative extrema,and (d) use a graphing utility to confirm your results.21. f(x) = x² – 4x22. f(x) = x² + 6x + 1023. f(x) = -2x² + 4x + 324. f(x) = -3x? – 4x – 225. f(x) = 2r + 3x² – 12x26. f(x) = x³ = 6x² + 1527. f(x) = (x – 1)*(x + 3)28. f(x) = (x + 2)°(x – 1)5 - 5x29. f(x) =30. f(x) = x* - 32x + 431. f(x) = x/3 + 132. f(x) = x²/3 – 433. f(x) = (x + 2)²/334. (x) = (x – 3)/335. f(x) = 5 - |x - 5|36. f(x) = |x + 3| - 137. f(x) = 2x +38. f(x)2r+ 139. f(x)40. f(x)9.[4-x.2r+ 1, x S -141. f(x) =42. f(x)2,|-2v,3x +1.43. ) =15 -A.44. /(x):++2v.46. flu) = (1De45. f() = (3-Je 347. /(x)=D 4(1aresin )48./C) = t aretan

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Answered: -- 2x + 1

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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Analyzing critical points Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points.
Approximating Relative Minima orMaxima In Exercises 49–54, use a graphingutility to approximate (to two decimal places)any relative minima or maxima of the function.49. f(x) = x(x + 3)50. f(x) = −x2 + 3x − 251. h(x) = x3 − 6x2 + 1552. f(x) = x3 − 3x2 − x + 153. h(x) = (x − 1)√x54. g(x) = x√4 − x
First Derivative Testa. Locate the critical points of f.b. Use the First Derivative Test to locate the local maximum andminimum values.c. Identify the absolute maximum and minimum values of the functionon the given interval (when they exist).
Finding the Derivative by the LimitProcess In Exercises 15–28, find the derivativeof the function by the limit process f (x) = x2 + x − 3
Verifying the Mean Value Theorem Determine whether the functionƒ(x) = 2x3 - 3x + 1 satisfies the conditions of the Mean Value Theorem on the interval [-2, 2]. If so, find the point(s) guaranteed to exist by the theorem.
Analyzing critical points Find the critical points of the following functions.Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, a local minimum,or a saddle point. If the Second Derivative Test is inconclusive,determine the behavior of the function at the critical points. ƒ(x, y) = -4x2 + 8y2 - 3
Finding the Derivative by the LimitProcess In Exercises 15–28, find the derivativeof the function by the limit process g(x) = −3
Determining Concavity In Exercises 3–14,determine the open intervals on which the graphof the function is concave upward or concavedownward.' 3. f (x) = x2 − 4x + 8
Finding the Derivative by the LimitProcess In Exercises 15–28, find the derivativeof the function by the limit process f (x) = 7x − 3
Finding the Derivative by the LimitProcess In Exercises 15–28, find the derivativeof the function by the limit process f (x) = −5x
Analyzing critical points Use the Second Derivative Test to classify the critical points of ƒ(x, y) = x2 + 2y2 - 4x + 4y + 6.
Find any critical points use the first derivative test to classify each critical point as a relative minimum, relative maximum, or neither (show work). 3.Use the second dertivative test to try to confirm the results from part ii (if the test is inconclusive, indicate this.) g(x) =x+1/x (Note: x=0 is not a critical point of this function, since it is not the domain, so you do not need to try to classify it as a local minimum or local maximum.)

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