Bài tập CALCULUS 03

Created by T Madas Question (**) The curve C has equation y = x3 − x − x + Find the x coordinates of the points on C with gradient x = − ,2 Created by T Madas Created by T Madas Question (**) y y = x3 − x + 16 x R O A x The figure above shows the cubic curve with equation y = x3 − x + 16 x , x ∈ » The curve meets the x axis at the origin O and at the point A a) Show clearly that x = at A The finite region R is bounded by the curve and the x axis b) Find the exact area of R C2N , 64 Created by T Madas Created by T Madas Question 10 (**) The point P (1,3) lies on the curve with equation y = f ( x ) , whose gradient function is given by f ′ ( x ) = x2 − x , x ∈ » Find an equation for f ( x ) C1F , f ( x ) = x3 − x + Question 11 (**) The curve C has equation y = x5 − x3 − 3x + 25 Find an equation of the tangent to C at the point where x = y = 5x − Created by T Madas