Answer:
a = 3
b = -12
Step-by-step explanation:
gradient function (y') = ax² + b
curve function (y) = 1/3 ax³ + bx + c
pass (1,-11) : -11 = 1/3 a + b + c ..... (1)
pass (2,-16) : -16 = 8/3 a + 2b + c ..... (2)
slope at (2,-16) is 0 (its tangent parallel to x axis)
at (2 , -16) ax² + b = 0 4a + b = 0 b = -4a .... (3)
(2) - (1) : -5 = 7/3 a + b = 7/3 a -4a = -5/3 a ... (4)
3 x (4) : -15 = -5a a = 3
b = -4a = -4 x 3 = -12
