00:01
In this question, the profit function px equals to 4x square minus 7 x square minus 6 upon x square plus 6 is given.
00:15
Now this function can be written as px equals to 4x square into 2 x square minus 4 x square into 6 minus 7 x square plus 42 upon x square plus 6.
00:37
Then after further simplifying px will be equals to 4x raise to the power 4 minus 24 x square minus 7 x square plus 42 upon x square plus 6 is given.
00:57
Then from here px will be equals to 4x to the power 4 minus 27 plus 4 that is 24 plus 7 that will be 31 x square plus 42 upon x square plus x 6.
01:19
Now differentiating both side, differentiating both side with respect to x using quotient rule, using quotient rule.
01:39
So from here p dash x will be equals to the function in the denominator which is x square plus 6 will be whole square and leaving this function x square plus 6 as it is d by dx of 4x to the power 4 minus 31 x square plus 42 and minus leaving this function as it is 4x square 4x to the power 4 minus 31 x square plus 42 into d by dx of x square plus 6.
02:23
Now from here we get p dash x equals to x square plus 6 into derivative of this function.
02:33
So this will be 16 x cube minus 62 x and plus 0 and this will be minus 4 x square minus 4 x to the power 4 minus 31 x square plus 42 into derivative of this function will be 2x plus 0 upon x square plus 6 whole square.
03:04
Then after further simplifying p dash x equals to x square plus that is 16 x cube minus 62 x minus this will be 4 x to the power 4 minus 31 x square plus 42 into 2x upon x square plus 6 whole square...