 Hi and welcome to the session, I am Shashi and I am going to help you with the following question. Question says, it is given that at x equal to 1 the function x raised to the power 4 minus 62 x square plus Ax plus 9 attains its maximum value on the interval 0 to find the value of A. First of all let us understand that if we are given a function f which is differentiable on closed interval i and sees any interior point of the closed interval i, then f dash c is equal to 0 if function f attains its absolute maximum value at c or simply we can say if function f attains its maximum value at c. This is the key area to solve the given question. Now let us start the solution. Let function f is given by fx equal to x raised to the power 4 minus 62 x square plus Ax plus 9. Now differentiating both sides with respect to x we get f dash x equal to 4x cube. We know derivative of x raised to the power 4 is 4x cube. Now derivative of 62 x square is 124x, derivative of Ax is A and derivative of 9 is 0. So we get f dash x equal to 4x cube minus 124x plus A. It is given in the question that at x equal to 1 the given function attains its maximum value on the interval 0 to. Now by key idea f dash 1 must be equal to 0. Now substituting 1 for x in this expression we get the value of f dash 1. So f dash 1 is equal to 4 multiplied by 1 cube minus 124 multiplied by 1 plus A equal to 0. On simplifying we get 4 minus 124 plus A equal to 0. Now we know 4 minus 124 is equal to minus 120. So we get minus 120 plus A equal to 0. Now adding 120 on both sides we get A is equal to 120. So our required value of A is 120. This is our required answer. This completes the session. Hope you understood the session. Take care and have a nice day.