 Hi, and how are you all? The question says five points at which the tangent to the curve y is equal to x cubed minus 3x square minus 9x plus 7 is parallel to the x-axis. Now here in this question we are given the equation of the curve as x cubed minus 3x square minus 9x plus 7. First of all let us differentiate y with respect to x. And I am doing so we get dy by dx is equal to 3x square minus 6x minus 9. Now we are given that the tangent is parallel to x-axis. Right, so this means that dy by dx should be equal to 0. Right, we have the value of dy by dx as 3x square minus 6x minus 9. So it will be equal to 0 or we have x square minus 2x minus 3 equal to 0. We have divided the equation by 3 or on splitting the middle term we have the factors as x minus 3 into x plus 1 is equal to 0. This implies that the value of x is either 3 or it is minus 1. Now let us find out the value of y when x is equal to 3. So the value of y when x is equal to 3 is 3 into 3 square minus 6 into 3 minus 9 which on solving gives us the answer as minus 20. And when x is equal to minus 1 then y is equal to 3 into minus 1 the whole square minus 6 into minus 1 minus 9 which is equal to 12. Hence the points at which the tangent to the curve y is equal to x cube minus 3x square minus 9x plus 7 is parallel to the x-axis r 3 minus 20 and minus 1, 12. Right, so this is the required answer to the given question. So understood whole procedure where do take care of your calculations and have a very nice day ahead.