Created by T Madas Question 123 (***+) −1 f ( x ) = x − x + 1 , x > Find the exact value of f ′ ( ) f ′ ( ) = 33 Question 124 (***+) The curve C has equation y= A +8 x , x > 0, x where A is a non zero constant The normal to the curve at C , at the point where x = , has gradient − Find the value of A A = 20 Created by T Madas Created by T Madas Question 125 (***+) Find the exact value of (3 + x ) dx , giving the answer in the form a + b , where a and b are integers + 16 Question 126 (***+) A cubic curve C passes through the points P ( −1, −9 ) and Q ( 2,6 ) and its gradient function is given by dy = x + kx + , dx where k is a non zero constant Find an equation for C C1Z , y = x3 − x + x + Created by T Madas Created by T Madas Question 127 (***+) y C y = + x − x − x3 A O x B The figure above shows part of the curve with equation y = + x − x − x3 The curve meets the x axis at A and B a) Verify that the coordinates of A are ( −2,0 ) and hence use algebra to show that the coordinates of B are ( 2,0 ) The point C is a stationary point of the curve b) Use calculus to determine the exact coordinates of C c) Find the exact area of the finite region bounded by the curve and the x axis ( ) C2E , C , 256 , area = 64 27 Created by T Madas ... show that the coordinates of B are ( 2,0 ) The point C is a stationary point of the curve b) Use calculus to determine the exact coordinates of C c) Find the exact area of the finite region bounded