Explanation Given information:- The given derivative of y = ( x 3 − 3 x ) 1 / 3 . Calculations:- The given derivative of y = ( x 3 − 3 x ) 1 / 3 . To find the transition point, interval of increase and decrease, concavity, and asymptotic behavior, we will take the first and second derivative of the given equation as shown below: y = ( x 3 − 3 x ) 1 / 3 . [The given derivative of the equation] y ' = d d x ( x 3 − 3 x ) 1 / 3 [Differentiate with respect to x ] y ' = 1 3 ( x 3 − 3 x ) 1 3 − 1 ⋅ d d x ( x 3 − 3 x ) [Apply power rule [ u ( x ) n ] ' = n ⋅ u ( x ) n − 1 ⋅ u ' ( x ) ] y ' = d d x [ x 3 ] − 3 ⋅ d d x [ x ] 3 ( x 3 − 3 x ) 2 3 [ ∴ , d d x [ x ] = 1 , d d x [ x 2 ] = 2 x ] y ' = 3 x 2 − 3 3 ( x 3 − 3 x ) 2 3 = x 2 − 1 ( x 3 − 3 x ) 2 3 Find the second derivative by using first derivative are as shown below: y ' = x 2 − 1 ( x 3 − 3 x ) 2 3 [Find the second derivative] y ' ' = d d x [ x 2 − 1 ( x 3 − 3 x ) 2 3 ] [Differentiate by the quotient rule [ u ( x ) v ( x ) ] ' = u ' ( x ) ⋅ v ( x ) − u ( x ) ⋅ v ' ( x ) v ( x ) 2 ] y ' ' = d d x [ x 2 − 1 ] ⋅ ( x 2 − 3 x ) 2 3 − ( x 2 − 1 ) ⋅ d d x [ ( x 2 − 3 x ) 2 3 ] ( ( x 2 − 3 x ) 2 3 ) 2 y " = ( d d x [ x 2 ] + d d x [ − 1 ] ) ( x 2 − 3 x ) 2 3 − 2 3 ( x 2 − 3 x ) 2 3 − 1 ⋅ d d x [ x 2 − 3 x ] ( x 2 − 3 x ) 4 3 y " =

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Author: Rogawski

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Chapter 4.5, Problem 32E

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Chapter 4.5, Problem 31E

Chapter 4.5, Problem 33E

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Consider the graphs of y = f(x) and y = g(x) in the given diagram y= f(x). y = g(x) Evaluate (f+g)(2) -5 Determine all for which g(x) < f(x) Determine all for which f(x) +3 = g(x)

I) For what value(s) of x does g(x) = -4? Separate multiple answers with commas as needed. J) Give the interval(s) of such that g(x) > 0. Use the union symbol between multiple intervals. K) Give the interval(s) of such that g(x) <0. Use the union symbol between multiple intervals.

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Chapter 4 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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Prob. 42E Ch. 4.5 - Prob. 43E Ch. 4.5 - Prob. 44E Ch. 4.5 - Prob. 45E Ch. 4.5 - Prob. 46E Ch. 4.5 - Prob. 47E Ch. 4.5 - Prob. 48E Ch. 4.5 - Prob. 49E Ch. 4.5 - Prob. 50E Ch. 4.5 - Prob. 53E Ch. 4.5 - Prob. 54E Ch. 4.5 - Prob. 55E Ch. 4.5 - Prob. 56E Ch. 4.5 - Prob. 57E Ch. 4.5 - Prob. 58E Ch. 4.5 - Prob. 59E Ch. 4.5 - Prob. 60E Ch. 4.5 - Prob. 61E Ch. 4.5 - Prob. 62E Ch. 4.5 - Prob. 63E Ch. 4.5 - Prob. 64E Ch. 4.5 - Prob. 65E Ch. 4.5 - Prob. 66E Ch. 4.5 - Prob. 67E Ch. 4.5 - Prob. 68E Ch. 4.5 - Prob. 69E Ch. 4.5 - Prob. 70E Ch. 4.5 - Prob. 71E Ch. 4.5 - Prob. 72E Ch. 4.5 - Prob. 73E Ch. 4.5 - Prob. 74E Ch. 4.5 - Prob. 75E Ch. 4.5 - Prob. 76E Ch. 4.5 - Prob. 77E Ch. 4.5 - Prob. 78E Ch. 4.5 - Prob. 79E Ch. 4.6 - Prob. 1PQ Ch. 4.6 - Prob. 2PQ Ch. 4.6 - Prob. 3PQ Ch. 4.6 - Prob. 1E Ch. 4.6 - Prob. 2E Ch. 4.6 - Prob. 3E Ch. 4.6 - Prob. 4E Ch. 4.6 - Prob. 5E Ch. 4.6 - Prob. 6E Ch. 4.6 - Prob. 7E Ch. 4.6 - Prob. 8E Ch. 4.6 - Prob. 9E Ch. 4.6 - Prob. 10E Ch. 4.6 - Prob. 11E Ch. 4.6 - Prob. 12E Ch. 4.6 - 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Chapter 4 Solutions