jika fungsi f(x) = a²x² - 12x + c² menyinggung sumbu x di x= 2/3 berapa a²- c² ?

jawab

f(x) = a² x² -12x + c²
menyinggung x di x = 2/3
y' = 0
2 a² x - 12 = 0
x = 2/3
2a² (2/3) = 12
a² = 12 : (4/3) = 9

f(x)= 9x² -12x + c²
f(2/3) = 0
9(2/3)² -12(2/3)+ c² =0
9(4/9) - 24/3 + c² = 0
4 - 8 + c² = 0
c² = 4

a² - c² = 9 - 4= 5