Explanation Given information: C ( x ) = ( 1 / 10 ) x 2 + 5 x + 300 . Formula used: The elasticity of the cost function C ( x ) at quantity x is, E c ( x ) = x ⋅ C ' ( x ) C ( x ) . Explanation: Let C ( x ) = ( 1 / 10 ) x 2 + 5 x + 300 Differentiate with respect to x : C ' ( x ) = d d x ( 1 10 x 2 + 5 x + 300 ) . By using the sum rule and the constant multiple rule, C ' ( x ) = 1 10 ⋅ d d x x 2 + 5 d d x x + d d x ( 300 ) . By using the power rule, = ( 1 / 10 ) ( 2 x ) + 5 ( 1 ) , = ( 1 / 5 ) x + 5 . Therefore, C ' ( x ) = x 5 + 5 = x + 25 5

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Chapter 5.3, Problem 27E

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To prove: Ec(50)<1 for C(x)=(1/10)x2+5x+300

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Chapter 5.3, Problem 26E

Chapter 5.3, Problem 28E

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To prove: E c ( 50 ) < 1 for C ( x ) = ( 1 / 10 ) x 2 + 5 x + 300

Solution Summary: The author explains the elasticity of the cost function C(x) at quantity x by using the sum rule and the constant multiple rule.

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To prove: Ec(50)<1 for C(x)=(1/10)x2+5x+300

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Chapter 5 Solutions

To prove: E c ( 50 ) &lt; 1 for C ( x ) = ( 1 / 10 ) x 2 + 5 x + 300

Solution Summary: The author explains the elasticity of the cost function C(x) at quantity x by using the sum rule and the constant multiple rule.

Videos

To prove: Ec(50)<1 for C(x)=(1/10)x2+5x+300

Want to see the full answer?

Chapter 5 Solutions

To prove: E c ( 50 ) < 1 for C ( x ) = ( 1 / 10 ) x 2 + 5 x + 300