(a) Explanation Proof: The unit price of the commodity is, P = f ( t ) = 6 + 4 e − 2 t . The function f ( x ) is increasing or decreasing, 1. If f ′ ( x ) > 0 for every value of x in ( a , b ) , then the graph of function is increasing on ( a , b ) . 2. If f ′ ( x ) < 0 for every value of x in ( a , b ) , then the graph of function is decreasing on ( a , b ) . Differentiate above equation with respect to t f ′ ( t ) = d d t ( 6 + 4 e − 2 t ) = d d t ( 6 ) + d d t ( 4 e − 2 t ) < (b) To determine To show: the graph of f is concave upward on ( 0 , ∞ ) . (c) To determine The value of lim t → ∞ f ( t ) . (d) To determine To sketch: The graph of given function f .

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Author: Tan

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Differential Equations

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Chapter 5.6, Problem 28E

(a)

To determine

To show: The function f is decreasing on interval (0,∞) .

(b)

To determine

To show: the graph of f is concave upward on (0,∞) .

(c)

To determine

The value of limt→∞f(t) .

(d)

To determine

To sketch: The graph of given function f.

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Chapter 5.6, Problem 27E

Chapter 5.6, Problem 29E

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Chapter 5 Solutions

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The function f is decreasing on interval ( 0 , ∞ ) .

Solution Summary: The author explains that the function f is decreasing on interval (0,infty).

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To show: The function f is decreasing on interval (0,∞) .

To show: the graph of f is concave upward on (0,∞) .

The value of limt→∞f(t) .

To sketch: The graph of given function f.

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Chapter 5 Solutions