Bài tập CALCULUS 08

Created by T Madas Question 29 (**+) y y = − x − x2 B A y=2 x O The figure above shows a quadratic curve and a straight line with respective equations y = − x − x and y =2 The points A and B are the points of intersection between the quadratic curve and the straight line a) Find the coordinates of A and B b) Determine the exact area of the finite region bounded by the quadratic curve and the straight line, shown shaded in the above figure MP1-A , A ( −2, ) , B (1, ) , area = Created by T Madas Created by T Madas Question 30 (**+) f ( x ) ≡ x3 − x + 3x + , x ∈ » Find the range of values of x , for which f ( x ) is decreasing C2I , < x < 3 Question 31 (**+) y=3x+ Show clearly that the value of d2y dx 27 , x∈», x > x where x = 27 , is 2187 proof Created by T Madas Created by T Madas Question 32 (**+) The curve C has equation y = 3x − x + x − , x ≥ Find an equation of the normal to C at the point where x = 7y + x +3 = Question 33 (**+) f ( x ) ≡ x + 10 + 25 , x ≠ x Find the coordinates of the two stationary points of f ( x ) and use f ′′ ( x ) to determine their nature C2K , ( 5, 20 ) , max ( −5,0 ) Created by T Madas