Bài tập CALCULUS 27

Created by T Madas Question 103 (***+) y y = x3 − x + 24 x + A L x O The figure above shows the graph of the curve C with equation y = x3 − x + 24 x + The straight line L is the normal to C at the point A , whose x coordinate is a) Show that an equation of L is x + y = 266 b) Show further that the area of the finite region bounded by C , L and the y axis is approximately 20 square units MP1-B , proof Created by T Madas Created by T Madas Question 104 (***+) The curve C has equation ( y = 1+ x a) Find an expression for ) , x≥0 dy dx The straight line L with equation y = 3x + is a tangent to C at the point P b) Use a calculus method to determine the coordinates of P C1X , Created by T Madas dy = 1+ , P ( 4,9 ) dx x Created by T Madas Question 105 (***+) y= x2 + , x ≠ 4x Find the range of values of x for which y is increasing C2W , x < −2 ∪ x > Created by T Madas ... x≥0 dy dx The straight line L with equation y = 3x + is a tangent to C at the point P b) Use a calculus method to determine the coordinates of P C1X , Created by T Madas dy = 1+ , P ( 4,9 )