00:01
In this question, given the function f' ' and given f ' of 1 and f of 1, we are asked to find f ' of x and f of x.
00:10
To get f ' of x, we need to integrate f' ' of x.
00:18
So we need to integrate xÂł minus 24x, and this equals to x to the fourth over 4 minus 24 multiplied by x squared over 2 plus the constant of integration c, and this simplifies to x to the fourth over 4 minus 12x squared plus c.
00:46
Now, to find the constant of integration c, we will use the f ' of 1 condition.
00:53
By the previous formula, f ' of 1 equals to 1 over 4 minus 12 plus c.
01:00
On the other hand, by the initial condition, f ' of 1 equals to 0.
01:07
From that equation, c equals to 12 minus 1 quarter, and 12 minus 1 quarter equals to 47 quarters.
01:21
Therefore, f ' of x equals to x to the fourth over 4 minus 12x squared plus 47 quarters.
01:33
So we found the formula for f ' of x.
01:39
Now let's find the formula for f of x.
01:42
To get f of x, we need to integrate f ' of x...