This question has a bit too many steps to be in standard O levels paper. Nonetheless, it is good practice for prelims ;)
A curve is defined by y = [(x - a)/(b - x)]½ where a < x =" (a" style="text-align: center;">*************************
Answer:
y = [(x - a)/(b - x)]½
y = (x-a)½ / (b-x)½
dy/dx = [ ½(x-a)-½(1)(b-x)½ - ½(b-x)-½ (-1)(x-a)½]/(b-x)
= ½(x-a)-½ (b-x)-½ [(b-x)+(x-a)]/(b-x)
= (b-a) / [2 (x-a)1.5 (b-x)1.5 )]
When x = (a+b)/2,
dy/dx = (b-a)/ {2[(b-a)/2]½][(b-a)/2]1.5}
= (b-a)/{2[(b-a)/2]²
= (b-a)/ ½(b-a)²
= 2 /(b-a) (shown)
