Okay, so this is a line l.
http://puu.sh/prQdV/8a46768079.jpg
It passes through points (a, a^2) (b, b^2) of the parabola y=x^2. ba
I was asked to find S1, so I did, it's 1/6 (b-a)^3
Then I was asked to find a in terms of b if l is perpendicular to the tangent line at b. It's (-1/2b) -b.
It says when 2 holds true, fins the minimum area of S in terms of b, for what value of b is the area simplified?
I'm really sorry for asking, but I asked a smart friend of mine and he told me that it's minimizes when b=a, is that true? I thought I had to derive S and set it equal to zero everytime, can anyone explain, please?
Thanks

Question

Okay, so this is a line l.
http://puu.sh/prQdV/8a46768079.jpg
 It passes through points (a, a^2) (b, b^2) of the parabola y=x^2. b>a
I was asked to find S1, so I did, it's 1/6 (b-a)^3
Then I was asked to find a in terms of b if l is perpendicular to the tangent line at b. It's (-1/2b) -b.
It says when 2 holds true, fins the minimum area of S in terms of b, for what value of b is the area simplified?
I'm really sorry for asking, but I asked a smart friend of mine and he told me that it's minimizes when b=a, is that true? I thought I had to derive S and set it equal to zero everytime, can anyone explain, please?
Thanks