 Hello and how are you all today? The question says find the points on the curve y is equal to x cube minus 11x plus 5 at which the tangent is y is equal to x minus 11. Now we are given the curve y's equation as x cube minus 11x plus 5 and the tangent is y equal to x minus 11. Now let us rewrite the equation to the curve once again. Now in differentiating y with respect to x we have 3x square minus 11. And here we have the equation of the tangent as x minus 11 on differentiating y with respect to x we have the answer as 1. So that means slope of the tangent is 1. Now we have the value of d by by dx as 1 so we can write that 3x square minus 11 is equal to 1 which implies 3x square equal to 12. Further implies x square is equal to 12 by 3 that is equal to 4. So we have x square equal to 4 giving us the value of x as plus minus 2. Now we know that when x is equal to 2 the value of y is equal to x minus 11 that is 2 minus 11 that is equal to minus 9. Now when the value of x is taken to be minus 2 the value of y is coming out to be minus 2 the whole cube minus 11 into minus 2 plus 5. We have substituted the value of x as minus 2 in this equation which is equal to 19. Now since tangent as minus 2 19 is not y equal to x minus 11 that means that when the value of x is minus 2 the value of y is coming out to be 19. But it is not corresponding to the equation of the tangent that is y is equal to x minus 11. So on ruling out this point we have the only answer as 2 comma minus 9. So this is the required answer to this question hope you understood it and have a nice day.