Bài tập CALCULUS 75

Created by T Madas Question 254 (****+) 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 ( ) C1W , a = , Q ,0 3 Created by T Madas Created by T Madas Question 255 (****+) The figure below shows the design of a window which is the shape of a semicircle attached to rectangle y 2x The diameter of the semicircle is x metres and is attached to one side of the rectangle also measuring x meters The other side of the rectangle is y metres The total area of the window is m a) Show that perimeter, P m , is given by P= (4 + π ) x + x b) Determine by differentiation an exact value of x for which P is stationary [continues overleaf] Created by T Madas Created by T Madas [continued from overleaf] c) Show that the value of x found in part (b) gives the minimum value for P d) Show that when P takes a minimum value x = y x= Created by T Madas ≈ 0.748 π +4