00:01
Hello students, to find the critical points of the function f of x is equal to x to the power 5 minus 10 x to the power 4 plus 30.
00:10
We will first find the first derivative that is f dash x then solve for x when f dash x is equal to 0.
00:16
So first f dash x is equal to d by dx of x to the power 5 minus 10 x to the power 4 plus 30 that is equal to 5 x to the power 4 minus 10 into 4 x to the power 3.
00:29
So 5 x to the power 4 minus 40 x cube.
00:34
So we have 5 x cube that is x minus 8.
00:40
So this gives us true critical points that is x is equal to 0 0 0 and 8 because x cube equal to 0 so 3 0s and x is equal to 8.
00:54
So we have 4 root that is 0 and 8.
00:59
So we can write critical points x is equal to 0 and 8.
01:10
Now moving forward to the second bit to find the inflection point we need to find where second derivative changes sign.
01:20
Let's find f double dash x.
01:21
So f double dash x is equal to 5 x to the power 4 minus 4 x cube.
01:32
So d by dx of 5 x to the power 4 minus 4 x cube.
01:37
So we have 20 x cube minus 120 x square that is equal to 20 x square equal to x minus 6.
01:53
So that gives us another critical point...