Created by T Madas Question 34 A curve C has equation y = x3 − x + a , x ∈ » , where a is a constant The tangent to C at the point where x = and the normal to C at the point where x = , meet at the point Q Given that Q lies on the x axis, determine in any order … a) … the value of a b) … the coordinates of Q ( ) a = , Q ,0 3 Created by T Madas Created by T Madas Question 35 The curve C has equation y= ( x3 x x − 128 x ) , x∈» , x>0 d3y dy d y a) Determine expressions for , and dx dx dx3 b) Show that the y coordinate of the stationary point of C is − k , where k is a positive integer d2y at the stationary point of C dx Give the answer in terms of c) Evaluate d) Find the value of MP1-M , d3y d2y at the point on C , where =0 dx3 dx d2y d3y dy − 12 2 , = 20 x3 − 320 x , = 60 x − 480 x = 120 x − 240 x , dx dx dx3 k = 3072 , 960 , 360 Created by T Madas ... the point on C , where =0 dx3 dx d2y d3y dy − 12 2 , = 20 x3 − 320 x , = 60 x − 480 x = 120 x − 240 x , dx dx dx3 k = 3072 , 960 , 360 Created by T Madas