Integral Problem: area of rectangle w/ vertices (x, lnx),...

[summersnow]

Let A(x) be the area of the rectangle whose vertices are (x, lnx) (10, lnx) (10, 0) and (x, 0) for [1,10] as shown in the figure above. *In the graph, y=lnx touches x-axis and (x, lnx)*

#1 - Write an expression for A(x) in terms of x.
#2 - Find the greatest value of A(x). Justify your answer.
#3 - Find the average value of A(x) on [1,10].

 

[skeeter]

Re: Integral Problem

Let A(x) be the area of the rectangle whose vertices are (x, lnx) (10, lnx) (10, 0) and (x, 0) for [1,10] as shown in the figure above. *In the graph, y=lnx touches x-axis and (x, lnx)*

#1 - Write an expression for A(x) in terms of x.

if I understand your description of the rectangle correctly ...
A(x) = base*height
A(x) = (10-x)*ln(x)
... that's the hard part, you try #2 & #3.[/color]

#2 - Find the greatest value of A(x). Justify your answer.
#3 - Find the average value of A(x) on [1,10].