Created by T Madas Question The point P ( 3, −1) lies on the curve with equation y = f ( x ) , whose gradient function is given by f ′ ( x ) = − x2 , x ∈ ℝ Find an equation for f ( x ) f ( x ) = + x − x3 Question By showing clear workings, find the value of ∫ x− dx x 80 Created by T Madas Created by T Madas Question The curve C with equation y = f ( x ) has gradient function dy = x2 + , x ≠ dx x The point A ( −1, −1) lies on C Find an equation for C y = x3 − −5 x Question ( ) y = x 6x − x , x ≥ By showing all steps in the workings, find an expression for ∫ y dx x3 − x + C Created by T Madas Created by T Madas Question The point P ( 4,9 ) lies on the curve with equation y = f ( x ) , whose gradient function is given by f ′( x) = 1+ , x >0 x Find an equation for f ( x ) f ( x) = x + x − Question 10 dy = 4+ , x ≠ dx x Given that y = when x = , express y in terms of x y = 4x − Created by T Madas +2 x