Explanation Given: The functions are f ( x ) = − x 2 + 4 x and g ( x ) = 2 x − 3 . Definition used : “Suppose that f and g are continuous functions with f ( y ) ≥ g ( y ) on the interval [ c , d ] . The area of the region bounded by the graphs x = f ( y ) and x = g ( y ) on [ c , d ] is A = ∫ c d ( f ( y ) − g ( y ) ) d y .” Calculation: The given functions are f ( x ) = − x 2 + 4 x and g ( x ) = 2 x − 3 . Substitute different real values of x in the given functions and form a table of x and function f ( x ) and g ( x ) to obtain coordinates, x f ( x ) = − x 2 + 4 x g ( x ) = 2 x − 3 − 1 − 5 − 5 0 0 − 3 1 3 − 1 2 4 1 3 3 3 The above given table gives the different ordered pairs to plot the graph of given function. Plot the graph of given function by joining all the ordered pairs by a smooth curve, Figure (1) Thus, the Figure (1) shows the graph of functions f ( x ) = − x 2 + 4 x and g ( x ) = 2 x − 3 . Equate functions f ( x ) = − x 2 + 4 x and g ( x ) = 2 x − 3 to find the point of intersection

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Author: Tan

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Chapter 6.6, Problem 36E

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Chapter 6 Solutions

EBK APPLIED CALCULUS FOR THE MANAGERIAL

Chapter 6.1, Problem 1CQ Chapter 6.1, Problem 2CQ Chapter 6.1, Problem 3CQ Chapter 6.1, Problem 4CQ Chapter 6.1, Problem 1E Chapter 6.1, Problem 2E Chapter 6.1, Problem 3E Chapter 6.1, Problem 4E Chapter 6.1, Problem 5E Chapter 6.1, Problem 6E

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Chapter 6.6, Problem 36E

Solution Summary: The author determines the sketch of the graph of f and g and finds the area completely enclosed under it. Substitute different real values of x in the given functions to obtain coordinates.

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