Explanation Consider equation of curve, − 12 x + x 3 + y + y 2 = 4 . Take the derivative of curve equation: d ( − 12 x + x 3 + y + y 2 ) = d ( 4 ) − 12 d x + d x 3 + d y + d y 2 = 0 − 12 d x + 3 x 2 d x + d y + 2 y d y = 0 ( − 12 + 3 x 2 ) d x + ( 1 + 2 y ) d y = 0 Solve for d y d x . d y d x = − ( − 12 + 3 x 2 ) ( 1 + 2 y ) Set d y d x = 0 or ( 1 + 2 y ) = 0 in order to find critical value. − ( − 12 + 3 x 2 ) ( 1 + 2 y ) = 0 − 12 + 3 x 2 = 0 x 2 = 4 and ( 1 + 2 y ) = 0 Solve for x , x = 2 and − 2 and y = − 0.5 Substitute the x = 2 and − 2 in the equation − 12 x + x 3 + y + y 2 = 4 . − 12 ( 2 ) + ( 2 ) 3 + y + y 2 = 4 − 24 + 8 + y + y 2 = 4 − 16 + y + y 2 = 4 y 2 + y − 20 = 0 and To determine (b) To find: Whether the critical points found in part (a) are relative maxima or relative minima by taking values of x nearby and solving for the corresponding values for y . To determine (c) To find: Whether the function has absolute maximum or minimum.

Pearson eText for Calculus for the Life Sciences -- Instant Access (Pearson+)

2nd Edition

ISBN: 9780137553457

Author: Raymond Greenwell, Nathan Ritchey

Publisher: PEARSON+

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Question

Chapter 6.CR, Problem 47CR

To determine

(a)

To find:

The critical points on the curve. −12x+x3+y+y2=4.

To determine

(b)

To find:

Whether the critical points found in part (a) are relative maxima or relative minima by taking values of x nearby and solving for the corresponding values for y.

To determine

(c)

To find:

Whether the function has absolute maximum or minimum.

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Chapter 6.CR, Problem 46CR

Chapter 6.CR, Problem 48CR

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Chapter 6 Solutions

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(a) To find: The critical points on the curve. − 12 x + x 3 + y + y 2 = 4 .

Solution Summary: The author explains how to find the critical points on the curve.

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(a)

To find:

The critical points on the curve. −12x+x3+y+y2=4.

(b)

To find:

Whether the critical points found in part (a) are relative maxima or relative minima by taking values of x nearby and solving for the corresponding values for y.

(c)

To find:

Whether the function has absolute maximum or minimum.

Want to see the full answer?

Chapter 6 Solutions

(a) To find: The critical points on the curve. − 12 x + x 3 + y + y 2 = 4 .

Solution Summary: The author explains how to find the critical points on the curve.

Concept explainers

Videos

(a) To find: The critical points on the curve. −12x+x3+y+y2=4.

(b) To find: Whether the critical points found in part (a) are relative maxima or relative minima by taking values of x nearby and solving for the corresponding values for y.

(c) To find: Whether the function has absolute maximum or minimum.

Want to see the full answer?

Chapter 6 Solutions

(a)

To find:

The critical points on the curve. −12x+x3+y+y2=4.

(b)

To find:

Whether the critical points found in part (a) are relative maxima or relative minima by taking values of x nearby and solving for the corresponding values for y.

(c)

To find:

Whether the function has absolute maximum or minimum.