Bài tập CALCULUS 14

Created by T Madas Question 55 (***) y C O P x The figure above shows the cubic curve C which meets the coordinates axes at the origin O and at the point P The gradient function of C is given by f ′ ( x ) = 3x − x + a) Find an equation for C b) Determine the coordinates of P C1H , f ( x ) = x3 − x + x , P ( 2,0 ) Created by T Madas Created by T Madas Question 56 (***) The point P ( 8,18) lies on the curve C , whose gradient function is given by dy = x − 10 , x ≥ dx Find an equation for C C1L , y = x − 10 x + Question 57 (***) A curve C has equation given by y= + 3x3 x2 , x≠0 Find the coordinates of the point on C where the gradient is (1, ) Created by T Madas Created by T Madas Question 58 (***) The temperature, T in °C , of a hot drink t minutes after it was made is given by T = 90 − 8t + t , ≤ t ≤ a) Calculate after how many minutes the drink has a temperature of 60 °C b) Find the rate of change of temperature of the drink minutes after it was made t = , −4 °C / Question 59 (***) Show clearly that  3 x− dx = k , x where k is an integer to be found k =2 Created by T Madas