Explanation Given: Function f ( x ) = 3 x 4 − 4 x 3 + 6 Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. Let us assume that p is the critical point of a continuous function f . Moving from left to right If p′ changes from negative to positive at p , then f has local minimum at p If p′ changes from positive to negative at p , then f has local maximum at p Calculation: Function is given as f ( x ) = 3 x 4 − 4 x 3 + 6 Derivative of above function is calculated as follows: f ′ ( x ) = d d x ( 3 x 4 − 4 x 3 + 6 ) f ′ ( x ) = 3 ( 4 x 3 ) − 4 ( 3 x 2 ) + ( 0 ) f ′ ( x ) = 12 x 3 − 12 x 2 In order to find the critical points, put f ′ ( x ) = 0 Thus, we have 12 x 3 − 12 x 2 = 0 12 x 2 ( x − 1 ) = 0 12 x 2 = 0 or x − 1 = 0 x = 0 or x = 1 Thus, critical points are x = 0 and x = 1 Now, f ′ ( − 1 )

6th Edition

ISBN: 9781119267874

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 4.1, Problem 22P

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To find all critical points for below function and then use first-derivative test to determine local maxima and minima. Also, check your answer by graphing

f(x)=3x4−4x3+6

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Chapter 4.1, Problem 21P

Chapter 4.1, Problem 23P

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Question 4 Find an equation of (a) The plane through the point (2, 0, 1) and perpendicular to the line x = y=2t, z=3+4t. 3t, (b) The plane through the point (3, −2, 8) and parallel to the plane z = x+y. (c) The plane that contains the line x = parallel to the plane 5x + 2y + z = 1. 1+t, y2t, z = 43t and is (d) The plane that passes through the point (1,2,3) and contains the line x = 3t, y=1+t, and z = 2 – t. (e) The plane that contains the lines L₁ : x = 1 + t, y = 1 − t, z = = L2 x 2s, y = s, z = 2. 2t and

can you explain why the correct answer is A

Chapter 4 Solutions

APPLIED CALCULUS-WILEYPLUS

Ch. 4.1 - Prob. 1P Ch. 4.1 - Prob. 2P Ch. 4.1 - Prob. 3P Ch. 4.1 - Prob. 4P Ch. 4.1 - Prob. 5P Ch. 4.1 - Prob. 6P Ch. 4.1 - Prob. 7P Ch. 4.1 - Prob. 8P Ch. 4.1 - Prob. 9P Ch. 4.1 - Prob. 10P

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To find all critical points for below function and then use first-derivative test to determine local maxima and minima . Also, check your answer by graphing f ( x ) = 3 x 4 − 4 x 3 + 6

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To find all critical points for below function and then use first-derivative test to determine local maxima and minima. Also, check your answer by graphing f(x)=3x4−4x3+6

Want to see the full answer?

Chapter 4 Solutions

To find all critical points for below function and then use first-derivative test to determine local maxima and minima. Also, check your answer by graphing

f(x)=3x4−4x3+6