Hmm...alternatively you can let , you should still obtain the same thing.
Daigo has just taken Algebra. Soon, i think the suggests should somewhat easier to understand; not calculus or trigonometry, but basic Algebra.
You should estimate the points on the graph that are max. and min.
Aha! I thought there would be an non-calculus, non-trig, algebraic solution to this problem.
Let k be the maximal value of so that . Cross-multiplying, we obtain
. We want k to be as large as possible subject to the constraint that x is real. This implies that
. The largest possible value of k is .
Furthermore, since is an odd function, the smallest possible value of k is .