Classify the critical points as relative maxima, relative minima, or horizontal points of inflection. In each case, check your conclusions with a graphing utility. (If an answer does not exist, enter DNE.)- **Relative maxima** \((x, y) = \left(1, \frac{29}{6}\right)\) Incorrect (✗)- **Relative minima** \((x, y) = \left(-2, \frac{28}{3}\right)\) Incorrect (✗)- **Horizontal points of inflection** \((x, y) = (DNE)\) Correct (✓) ### Consider the following function:\[ y = \frac{x^3}{3} + \frac{x^2}{2} - 2x + 6 \]#### (a) Find \( y' = f'(x) \).\[ f'(x) = x^2 - 1 \]*Incorrectly computed.*#### (b) Find the critical values.(Enter your answers as a comma-separated list.)\[ x = 1, -1 \]*Incorrectly computed.*#### (c) Find the critical points.\[ (x, y) = \left(1, \frac{16}{3}\right) \](Smaller \( x \)-value)\[ (x, y) = \left(-1, \frac{20}{3}\right) \](Larger \( x \)-value)*Incorrectly computed.*#### (d) Find intervals of \( x \)-values where the function is increasing.(Enter your answer using interval notation.)\[ (-\infty, -1), (1, \infty) \]*Incorrectly computed.*#### Find intervals of \( x \)-values where the function is decreasing.(Enter your answer using interval notation.)\[ (-1, 1) \]*Incorrectly computed.*

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Answered: Consider the following function. x3 + y…

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 functions ƒ and g are differentiable and h(x) = f(g(x)). Use the information below to find h' (2). f(2) = -1 f' (2) = 3 f'(1) = 4 g'(2) = -1 9(-6) — 6 д'(-6) — —3 f(1) = -6 g(2) 1 а) О4 b) O-8 c) 00 d) O1 e) О-4
хуz 1+x+y*+z" Suppose that the height of a hill above sea level is given by S(x,y.z) = where x, y and z are in meters. A climber is standing at (1,2,3). a. In what direction climber should walk to reduce his height from sea level. b. Find the derivative if climber moves toward (1,1,1)
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Consider the following function. x3 + y = x2 2x + 6 3 2 (a) Find y' = f'(x). f'(x) 1 = (b) Find the critical values. (Enter your answers as a comma-separated list.) X = 1, – 1 - (c) Find the critical points. (1,- 16 3 (х, у) 3D (smaller x-value) 20 (x, y) = (–1, (larger x-value) | 3