Bài tập CALCULUS 16

Created by T Madas Question 64 (***) y = x − x4 , x ∈ » a) Find the coordinates of the stationary point of y and determine its nature b) Show clearly that y has no points of inflection ( ) C2N , max , Question 65 (***) dy = 4+ , x ≠ dx x Given that y = when x = , express y in terms of x C1Q , y = x − Created by T Madas +2 x Created by T Madas Question 66 (***) y L y= x P R O x The figure above shows the graph of the curve C with equation y= x , x≥0 The point P lies on C where x = The straight line L is the tangent to C at P a) Find an equation of L The finite region R , shown shaded in the figure, is bounded by C , L and the x axis b) Find the exact area of R MP1-D , y = x + , Created by T Madas Created by T Madas Question 67 (***) The curve C has equation f ( x) = ( x − 3)( x + ) , x x >0 a) Express f ( x ) in the form Ax + Bx + Cx − 12 , where A , B and C are constants to be found b) Show that the tangent to C at the point where x = is parallel to the line with equation y = 13 x + A = , B = , C = −6 Created by T Madas