Drawing the graphs first will greatly aid in their
interpretation!
Key to this problem is the idea for small values of t we have t
is a lot larger than t^2, which is in turn a lot larger than
t^3. For large values of t the reverse is
true.
Show without recourse to any calculating aid that 7^{1/2} + 7^{1/3}
+ 7^{1/4} < 7 and 4^{1/2} + 4^{1/3} + 4^{1/4} > 4 . Sketch
the graph of f(x) = x^{1/2} + x^{1/3} + x^{1/4} -x