▁defined ▁for ▁, ▁where ▁ ▁is ▁a ▁constant , ▁and ▁a ▁quart ic ▁function ▁ ▁of ▁which ▁leading ▁coefficient ▁is ▁ ▁satisfy ▁the ▁three ▁conditions ▁below : ▁ ▁A ) ▁For ▁all ▁real ▁numbers ▁, ▁such ▁that ▁, ▁. ▁ ▁B ) ▁For ▁two ▁different ▁real ▁numbers ▁ ▁and ▁, ▁ ▁has ▁the ▁same ▁local ▁maximum ▁ ▁at ▁ ▁and ▁. ▁() ▁ ▁C ) ▁ ▁has ▁more ▁local ▁ext re ma ▁than ▁ ▁does . ▁ ▁. ▁Find ▁the ▁minimum ▁of ▁. Bel ow ▁is ▁the ▁ 2 9 th ▁problem ▁in ▁Mathemat ics ▁subject ▁for ▁all ▁applic ants ▁of ▁CS AT ▁held ▁in ▁ 1 9 9 6 ▁that ▁is ▁considered ▁to ▁be ▁the ▁hard est ▁one ▁in ▁history . ▁It ▁had ▁correct ▁response ▁rates ▁of ▁ 0 . 0 8 %. If ▁two ▁equations ▁ ▁and ▁ ▁have ▁ 7 ▁and ▁ 9 ▁solutions ▁respectively ▁and ▁a ▁set ▁is ▁an ▁infinite ▁set , ▁, ▁the ▁number ▁of ▁elements ▁in ▁' s ▁subset , ▁var ies ▁according ▁to ▁the ▁values ▁of ▁ ▁and ▁. ▁Find ▁the ▁maximum ▁of ▁. ▁ ▁Ge ometry ▁and ▁Vector ▁ ▁Below ▁is ▁the ▁ 2 9 th ▁problem ▁in ▁Mathemat ics ▁subject ▁type ▁B , ▁previous ▁name ▁of ▁type ▁Ga , ▁of ▁CS AT ▁held ▁in ▁ 2 0 1 3 . ▁and ▁ ▁are ▁points ▁on ▁the ▁sphere ▁. ▁ ▁and ▁ ▁are ▁the ▁fo ots ▁of ▁two ▁per pend icular s ▁from ▁ ▁and ▁ ▁to ▁the ▁plane ▁ ▁respectively . ▁ ▁and ▁