Determine the concavity in the graph of f (x) = -4x^3 + 8x^2 + ax + b, where a and b are real numbers.
Answer
downward on (-∞, ∞)
downward on (-∞, 2/3);
upward on (2/3, ∞)
upward on (-∞, -2/3);
downward on (-2/3, ∞)
upward on (-∞, 2/3);
downward on (2/3, ∞)
f' = -12 x^2 + 16 x + a
f" = -24 x + 16
sheds water when when f" is negative
holds waster when f" is positive
f" is 0 when x = 2/3
sheds water when x < 2/3
holds water when X>2/3
so B