the question is
Let F(a) be the function which gives the area under the graph of y=x*e^-x between x=0 and x=a for a>0
i found F(a) to be (-x*e^-x)-(e^-x)
then evaluated with the given endpoints i got
(-a*e^-a)-e^a+1
(not sure if this is correct)
the second question is
is F increasing or a decreasing function?
is it the same that if the second derivative tells the concavity? pointers anyone?
Hello, acosta0809!
It's correct!Let be the function which gives the area under the graph of
between and for
i found to be: .
then evaluated with the given endpoints i got: .
(not sure if this is correct)
Find the first derivative (slope).The second question is:
Is an increasing or a decreasing function?
We have: .
Then: .
Since , then: . is always positive.
Therefore, is an increasing function.
If we look at the graph, it's obvious . . .As increases, the area under the curve increases.Code:. . . - | . . . - | ..*. . . . - | *::::::*. . . . - | *::::::::::*.. . . . - |*::::::::::::::::* . . . - |:::::::::::::::::| * . . . - * - - - - - - - - + - - - - - . . . - | a