This is from the 1998 NEAP 2U Trial:
Consider the function f(x) = ax^3 + bx^2 +cx + d, where a, b, c and d are constants.
The graph of y = f(x) has a minimum turning point, P, at x = 0; a point of inflexion, Q, at (1,1); and a maximum turning point, R, at (2,3).
a) Find f'(x) and show that c = 0.
b) Find f''(x) and hence show that b = -3a
c) By considering the coordinates of Q and R, show that d - 2a = 1 and d - 4a = 3
d) Hence find the values of the consonants a and d
Please help with solutions. Thanks!
Consider the function f(x) = ax^3 + bx^2 +cx + d, where a, b, c and d are constants.
The graph of y = f(x) has a minimum turning point, P, at x = 0; a point of inflexion, Q, at (1,1); and a maximum turning point, R, at (2,3).
a) Find f'(x) and show that c = 0.
b) Find f''(x) and hence show that b = -3a
c) By considering the coordinates of Q and R, show that d - 2a = 1 and d - 4a = 3
d) Hence find the values of the consonants a and d
Please help with solutions. Thanks!