Bài tập CALCULUS 19

Created by T Madas Question 75 (***) The curve C has equation y = x5 − , x ≥ Show clearly that x2 d2y dx − 15 y = k , where k is an integer to be found C1E , k = 15 Question 76 (***) f ′ ( x ) = ( 3x − 1) Given that f ( 3) = 56 , find an expression for f ( x ) C1N , f ( x ) = 3x3 − 3x + x − Created by T Madas Created by T Madas Question 77 (***) A 8x 6x E B y D 10 x C The figure above shows a pentagon ABCDE whose measurements, in cm , are given in terms of x and y a) If the perimeter of the pentagon is 120 cm , show clearly that its area, A cm , is given by A = 600 x − 96 x b) Use a method based on differentiation to calculate the maximum value for A , fully justifying the fact that it is indeed the maximum value SYN-S , Amax = 937.5 Created by T Madas Created by T Madas Question 78 (***) y B y = x2 − x + A R y = 3x O P x The figure above shows the graph of the curve C with equation y = x2 − x + , x ∈ » intersected by the straight line L with equation y = 3x , x ∈ » The curve meets the straight line at the points A and B The point P is located on the x axis so that the straight line segment BP is parallel to the y axis The finite region R is bounded by C , L , BP and the x axis Show that the area of R , shown shaded in the figure, is 39 MP1-J , proof Created by T Madas