Question

How do you sketch this graph? Sketch the graph of y=xlnx

Answer 1

If I were given no restrictions on how to do it I would simply just use a graphics calculator and draw a sketch from that.

Answer 2

Thank you! omgg I'm so silly..
I see I see... But it is possible to do this question without a gc?

Answer 3

The graph seems to be a slightly retricemetrical bump below the x-axis, hanging from (0,0) and (1,0). The "bottom" is at, about, -1/3 (near x=1/3, actually). If you "ask" your computer or calculator for the value of x·ln(x) at x=0, however, there will be some sort of complaint rather than a number. The machines have been advised that 0 is not in the domain of ln. But the graph certainly seems to indicate that (0,0) is there (wherever there is!). What's going on?

Answer 4

multiply the graphs of y=x and y =lnx. when x is negative, there is no graph for y=lnx.. so y=xlnx is undefined when x is negative

Answer 5

Thank you! omgg I'm so silly..
I see I see... But it is possible to do this question without a gc?

Answer 6

oh so the restriction is actually due to the "ln" function is it? Like how you cant ln a negative number and zero?

Answer 7

note when x = 0, xlnx = 0.. and when x = 1, lnx = 0, so xlnx = 0

Answer 8

yes, xlnx is undefined when x is negative, since lnx is undefined when is negative

Answer 9

Just note that ln 0 is actually undefined. ln x is defined by
\[\int\limits_{1}^{x}1/t dt\] If you substitute zero into this equation, you will have 1/0, which is an undefined value.