Question 3
Let $k$ be a real number. Find the least value of $k$ such that the following inequality is correct:
$$\sqrt{x-2}+\sqrt{7-x}\le k.$$
Interpretation for this practice: the inequality must hold for every real $x$ for which both radicals are defined, namely $2\le x\le7$. The source leaves this quantifier implicit.
$$\sqrt{x-2}+\sqrt{7-x}\le k.$$
Interpretation for this practice: the inequality must hold for every real $x$ for which both radicals are defined, namely $2\le x\le7$. The source leaves this quantifier implicit.