Homework Soursedetermine the shortest distance from the ordered pair 14 to
determine the shortest distance from the ordered pair (1,4) to the graph y=x^2
Solution
point on graph is (x,y)
distance between graph and (1,4) is D=[(x-1)2+(y-4)2]
y=x2
D=[(x-1)2+(x2-4)2]
distance is minimum if f(x)=(x-1)2+(x2-4)2 is minimum
f \'(x)=0
2(x-1)+2(x2-4)2x =0
2x-2 +4x3-16x =0
4x3-14x-2 =0
by calculator x=1.93854
shortest distance =D=[(1.93854-1)2+(1.938542-4)2]
shortest distance =D=0.94 units
