If the graph of y=ax^3 +4x^2+cx+d has a point of inflection at (2,0), then what is the value of a?

1 Answer
Jan 9, 2018

#a=-2/3#

Explanation:

We have:

# y = ax^3 +4x^2+cx+d #

Differentiating we find the first and second derivatives:

# y' \ \ = 3ax^2 +8x+c #
# y'' = 6ax +8 #

For a point of inflection at #(2,0)# we require that #y''(2) = 0#, thus:

# :. 6x(2) + 8 = 0 => a=-2/3#