0:00
Hi there.
00:01
So for this problem, we need to find the function f of x such that it is described by the given initial value problem.
00:15
So we are given that the second derivative of this function should be equal to zero.
00:22
And the first derivative evaluated in 1 is equal to 1, and also we are given that the function evaluated in 1 is equal to minus 2.
00:45
Now, from the first condition, we know that this function cannot have an order greater than 1.
00:59
That's because if the function, for example, will be x squared, then when we integrate twice, we will obtain a number, which is different than zero.
01:13
So from that, we can say that the function that we are looking for should have the form of a, which is a number that we need to obtain, times x, and this plus b.
01:27
So we now, with the other two conditions, we need to determine the values of a and b.
01:33
Now, we are going to take the derivative of this function.
01:37
Well, as you can see, this satisfies the first condition, because if we take the first derivative of this function, that is going to be equal to a.
01:47
And if we take the second derivative of this function, it just simply equals to zero, because we know that the derivative of a constant is of an integer or a constant.
01:57
Is equal to 0.
01:59
So that satisfies the first condition.
02:04
Now with the first derivative evaluated at 1, we can obtain this is equal of 1, as you can see in here...