Higher Derivatives

Question

Which point on the curve y= x^2 is nearest do the point (3,0)

Answer 1

You can just use the distance formula, and then take the derivative, set it equal to 0 and solve.

D = [(x-3)² + (y-0)²)^1/2     but y = x²  so you can substitute

D = [(x-3)² + (x²)² ]^1/2

D = (x²-6x+9+x⁴)^1/2

D' = 1/2 *(x²-6x+9+x⁴)^-1/2 * (2x-6+4x³)

 

So when is the numerator = 0?

4x³+2x-6-0 has one real solution at x=1

plugging this in to the original equation, your point is (1,1).

 

Hope this helped.