Created by T Madas Question 184 (****) non calculator 48 + x y= , x>0 x2 a) Find an expression for dy dx b) Show that the value of dy where x = , is dx 64 dy − 23 = x − 24 x −3 dx Question 185 (****) non calculator ( ) f ( x ) = x x − 12 x − 16 , x > Find the exact value of f ′ ( ) f ′ (8) = Created by T Madas Created by T Madas Question 186 (****) A curve C has equation y= x −2 x2 , x>0 a) Find the coordinates of the stationary point of C , and determine its nature The curve has a non stationary turning point, P b) Determine the coordinates of P ( max at (1,1) , P 25 , 112 16 125 Created by T Madas ) Created by T Madas Question 187 (****) y O y= A x − 10 x + x2 B R x The figure above shows the graph of the curve with equation y= x − 10 x + x2 , x>0 The curve meets the x axis at the points A and B The finite region R , shown shaded in the figure above, is bounded by the curve and the x axis Find the exact area of R 16 Created by T Madas