00:00so here we have a question
00:00which is a fake value
00:03which is a constant
00:06which is a constant value
00:07which is a minimum
00:09now we know
00:11quadratic equation
00:13minimum value
00:14we find the differentiation
00:16zero equate
00:18quadratic equation
00:21graph
00:21this type
00:24x is positive
00:26x is positive
00:28infinity
00:32infinity
00:33infinity
00:33infinity
00:33square
00:35negative
00:39this type
00:42intersect
00:44we don't know
00:47that intersect
00:48now
00:48this slope
00:52so here is slope 0 and in the position of slope 0 will be the minimum value
01:00and in the question of minimum value and slope 0 will be the slope is equal to dy by dx
01:10so dy by dx x square 2x plus kx square k plus k square 0
01:23constant constant differentiation 0 is equal to 0
01:28so kx value value k is equal to minus 2x
01:38so this function minimum value find
01:42x value value x is equal to minus k by 2
01:50now if I see minimum value find
01:52x is equal to this function
01:55so this function of minus k
02:01minus k into minus k
02:04k square upon 2 into 2
02:06plus minus k upon 2 into k
02:10minus k square upon 2 plus k square
02:17This message minus
02:20So this is LCM
02:21So this is minus
02:22K square upon 4
02:25Plus K square
02:27LCM
02:28So this is 2
02:29Multiply
02:29Minus
02:302K square
02:31Plus K square
02:32Minus
02:33K square upon 4
02:35Plus K square
02:36LCM
02:384K square
02:39Minus
02:40K square upon 4
02:42Answer
02:433K square
02:45Upon 4
02:46Load it
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