00:01
In the given question, we have to find the stationary point where we have given the first function is y is equal to 3 times x to the power 4 minus 10 times x q plus 6 times x squared plus 5.
00:21
Now to find the stationary point, let's differentiate y with respect to x.
00:30
Therefore we have d .y over d x or y dash is a different.
00:35
Equals to 3 times 4 times x q minus 10 times 3 times x squared plus 6 times 2 times x plus 5 which simplifying use us therefore we have y dash is equals to 12 times x q minus 30 times x square plus 12 times 6 now to find the stationary point, we need to set the derivative of y -dash is equal to 0.
01:19
So this gives us 12 times x cubed minus 30 times x square plus 12 times x is equal to 0.
01:28
So simplifying it by taking 6 times x common from each term, we get 2 times x squared minus root x.
01:39
Here, sorry, we have 5 times root x plus 2 is equal to 0.
01:49
That gives us x is equal to 0 and 2 times x squared minus 5 times, sorry it is not root x.
02:01
Here we have x only minus 5 times x plus 2 is equal to 0.
02:08
That is we have x is equal to 0 and 2 times x times x minus 2 minus 1 times x minus 2 is equal to 0.
02:21
Simplifying it we get x minus 2 times 2 minus 1 is equal to 0.
02:28
That is we have x is equal to 0, x is equal to 2, x is equal to 1 over 2...