Question

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, ∞)

Answer 1

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