 Hi, and welcome to the session. I am Deepika here. Let's discuss the question. Find the approximate value of f of 5.001 where fx is equal to x cube minus 7x square plus 15. So let's start the solution. Given fx is equal to x cube minus 7x square plus 15. Therefore, f dash x which is equal to dy by dx is equal to 3x square minus 14x. Let x is equal to 5 and delta x is equal to 0.001. Then f of x plus delta x is equal to x plus delta x cube minus 7 into x plus delta x whole square plus 15 and delta y is equal to f of x plus delta x minus fx. This implies f of x plus delta x is equal to f of x plus delta y. This implies f of x plus delta x is equal to fx which is equal to x cube minus 7x square plus 15 plus dy by dx into delta x. And this is equal to x cube minus 7x square plus 15 plus dy by dx is equal to 3x square minus 14x into delta x. Therefore, f of 5.001 is equal to 5 cube minus 7 into 5 square plus 15 plus 3 into 5 square minus 14 into 5 into delta x which is 0.001 and this is equal to 125 minus 7 into 25 plus 15 plus 3 into 25 minus 70 into 0.001 and this is equal to 125 minus 175 plus 15 plus 75 minus 70 into 0.001 and this is equal to minus 35 plus 0.005. Therefore, f of 5.001 is equal to minus 34.995. Hence the answer for the above question that is approximate value of f of 5.001 is minus 34.995 and this is our answer. I hope the question is clear to you. Bye and take care.