Explanation y = x 5 2 − x 2 ( x > 0 ) x 5 2 − x 2 : x = 0 , x = 16 25 Find where f ’ ( x ) is equal to zero or undefined ( x ) = 5 x 3 2 2 − 2 x d d x ( x 5 2 − x 2 ) Apply the sum difference rule ( f ± g ) ' = f ' ± g ' = d d x ( x 5 2 ) − d d x ( x 2 ) d d x ( x 5 2 ) = 5 x 3 2 2 d d x ( x 5 2 ) Apply the power rule d d x ( x a ) = a ⋅ x a − 1 = 5 2 x 5 2 − 1 Simplify 5 2 x 5 2 − 1 : 5 x 3 2 2 5 2 x 5 2 − 1 Join 5 2 − 1 : 3 2 5 2 − 1 Convert elements to fraction 1 = 1 1 = − 1 1 + 5 2 Find the LCD for − 1 1 + 5 2 : 2 Find the least common denominators 1 ⋅ 2 = 2 2 Adjust fraction based on the LCD = − 1 ⋅ 2 2 + 5 2 Since the denominators are equal combine the fraction a c ± b c = a ± b c = − 1 ⋅ 2 + 5 2 − 1 ⋅ 2 + 5 = 3 Multiply the numbers − 1 ⋅ 2 + 5 1 ⋅ 2 = 2 =3 = 3 2 = x 3 2 Multiply fraction a ⋅ b c = a ⋅ b c = 5 x 3 2 2 = 5 x 3 2 2 d d x ( x 2 ) = 2 x d d x ( x 2 ) Apply the Power Rule : d d x ( x a ) = a ⋅ x a − 1 = 2 x 2 − 1 Simplify =2x = 5 x 3 2 2 − 2 x Solve <

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.3, Problem 38E

To determine

y=x52-x2 (x>0)

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Chapter 4.3, Problem 37E

Chapter 4.3, Problem 39E

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Chapter 4 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

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