Explanation Given: The given function is f ( x ) = 1 2 x 2 − 2 x + 4 . Definition used: If the derivative of function f ′ ( x ) changes sign from positive to negative as the graph of the function move across a critical number c , then function f has relative maximum at x = c . If the derivative of function f ′ ( x ) changes sign from negative to positive as the graph of the function move across a critical number c , then function f has relative minimum at x = c . Calculation: To get the relative minimum and maximum values first find the derivative of function. d d x f ( x ) = d d x ( 1 2 x 2 − 2 x + 4 ) = d d x ( 1 2 x 2 ) − d d x ( 2 x ) + d d x ( 4 ) = x − 2 The derivative of function is f ′ ( x ) = x − 2

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Chapter 4.1, Problem 56E

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The relative maximum and relative minimum for the function f(x)=12x2−2x+4 .

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Chapter 4.1, Problem 55E

Chapter 4.1, Problem 57E

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APP CAL MANAGE,LIFE,SOC STUD WEB ASSIGN

Ch. 4.1 - Explain each of the following: a. f is increasing...Ch. 4.1 - Prob. 2CQ Ch. 4.1 - Prob. 3CQ Ch. 4.1 - Prob. 4CQ Ch. 4.1 - Prob. 5CQ 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

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The relative maximum and relative minimum for the function f ( x ) = 1 2 x 2 − 2 x + 4 .

Solution Summary: The author calculates the relative maximum and relative minimum values for the function f(x)=12x

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The relative maximum and relative minimum for the function f(x)=12x2−2x+4 .

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Chapter 4 Solutions