=0 ⇒3t2−3t−(4−11t+6t2)=0 ⇒‌‌3t2−8t+4=0 ⇒‌‌3t2−6t−2t+4=0 ⇒‌‌3t(t−2)−2(t−2)=0 ⇒‌‌(t−2)(3t−2)=0 ∴‌‌t−2=0 or 3t−2=0 t=2 or t=2∕3 sin‌x=2 or sin‌x=‌
2
3
x=sin−1(‌
2
3
) Also, y=‌
4−3t
t−t2
=‌
4−3×2∕3
2
3
−(‌
2
3
)2
y=9 [∵sin‌θ≤1] [∵t=2∕3] Now, required graph is
From the graph, minimum value of f(x)≥9 α≥9 ∴α has minimum value 9 .