00:01
In this question, we are given a function, y is equal to x minus 4 square root of x.
00:08
We need to obtain the critical points of this function and determine the local maxima and local minimum.
00:22
Now, for that, let us first differentiate the given function.
00:26
First of all, the unit function can be written as y is equal to x minus 4 x raised to power 1 over 2.
00:33
Differentiating with respect to x, we get d -y over dx is equal to 1 minus 4 over 2 square root of x.
00:42
That is 1 minus 2 over square root of x.
00:46
Equating it with 0, we get 2 over square root of x is equal to 1.
00:53
That is 2 is equal to square root of x.
00:57
Therefore, squaring both sides, we get the value of x as 4.
01:07
Therefore this is the critical point.
01:13
Now we need to check whether it is a point of maximum or a point of minimum...