00:01
All right, so let's start by saying that our function p of x is going to be equal to a x squared plus b x plus c.
00:12
So our problem now is to basically solve for a, b, and c.
00:18
We can pretty easily do this since we're given specific points on each of the function, the first and the second derivative.
00:32
So let's first see that p of 2 is going to be 4a plus 2b plus c and we know that's going to be equal to 5.
00:43
Let's go ahead and calculate our first derivative then, which is going to be 2ax plus b.
00:54
And we now, we know that the first derivative at 2 .2 is 4a plus b and we know that that's going to be equal to three.
01:18
Let's go ahead now and calculate the second derivative, which is going to be equal to 2a, and we know that the second derivative at 2, which is equal to 2a is equal to 2.
01:37
So now we have these three equations to solve for the three variables, 4a plus 2, b plus c is equal to 5.
01:49
And then our next one is 4a plus b is equal to 3.
01:55
And then we have 2a is equal to 2.
01:59
So we basically just want to go ahead and now solve this system of equations...