Question

5) Find the point (L,y) on the graph of y= Vr nearest the point (1,0).

Answer 1

y = 5x suppose that (x,y) is nearest to the point (1,0). Distance between the two pintor V2-x)? H0-y)? Substitute y = 5x Distance = √(1-x)² + x Consider, f(x)=(1-x)²+* =1+x? 2n+ =1+² x f'(x) = 2x-1, f'(x) = 0 f"(x)=2 2x-1=0 x= 1/2 f"( 12) = 270 x

. f(x) is minimum when x= 1/2 When f(x) is minimum, the distanie is minimum . Minimum distance: √(1-1½)² + 1 = V / 4 + 1/2 √3/4 Anower