00:01
Hi, in this question, given that the function is f of x equals x square plus px plus q, we need to find the values of p and q.
00:17
Here given that f of 1 equals 3, extreme value of an f and 0 comma 2 is this value of minimum or maximum.
00:33
So that first we have to differentiate this to find the critical point.
00:41
So f dash of x equals 2x plus p so that we have to equate with 0.
00:54
F dash of x equals 0 so 2x plus p equals 0.
00:59
2x equals minus p and x equals minus p by 2.
01:05
Here given that x equals 1 then extreme value of f of x so that x equals 1 which implies 1 equals minus p by 2.
01:20
So 2 equals minus p.
01:24
Therefore, p equals minus 2.
01:28
Next we need to find the value of q.
01:31
So before that here f of 1 equals 3 is an extreme value of f of x...