Hi,
You may use GC to sketch the graph of y = x - ln x,
since it is a non-standard function.
Thanks.
Cheers,
Wen Shih
Afternote: One can sketch the graph of y = x - ln x without GC,
with basic knowledge of curve sketching.
1. Find x-intercepts, i.e. let y = 0. Then x = ln x, but no such
x exists since y = x and y = ln x do not intersect at all.
2. Find y-intercepts, i.e. let x = 0. This is not possible
because ln x is not defined when x = 0. Therefore, x = 0 is a
vertical asymptote. Note also, that x cannot take negative values,
since ln x will not be defined.
3. Investigate the behaviour as x approaches infinity. When that
happens, we observe that y approaches x, so y = x is an oblique
asymptote.
4. Determine stationary points by differentiation, i.e. let
dy/dx = 0. In this case, we have dy/dx = 1 - 1/x, from which x = 1
when dy/dx = 0. It is not difficult to ascertain that x = 1 gives a
minimum turning point by the second derivative test.
With these facts, we can go ahead and sketch the graph of y = x
- ln x.
Thanks again.