12.補充一個拙見
\(\displaystyle f(x)=-x \pm \sqrt{1-x}\)
case 1. if \(\displaystyle f(x)=-x + \sqrt{1-x} , -1\leq x\leq 1\)
微分畫圖可知圖形嚴格遞減 最大值在\(\displaystyle (-1,1+\sqrt{2})\),最小值在\(\displaystyle (1,-1)\)
case 2. if \(\displaystyle f(x)=-x + \sqrt{1-x} , -1\leq x\leq 1\)
畫圖可以知道
端點為\(\displaystyle (1,-1),(-1,1-\sqrt{2})\),最小值為\(\displaystyle (\frac{3}{4},-\frac{5}{4})\)
兩者取聯集,可得\(\displaystyle -\frac{5}{4}\leq a \leq 1+\sqrt{2}\)