Find the intervals of concavity for the function f (x) = x^3 + 3x^2 + 1

Answer 1

Find the 2nd derivative

f''(x) = 6x + 6

set it equal to zero & solve for x = -1

for x<-1 f(x) is concave downward

for x>-1 f(x) is concave upward

at x=-1, concavity changes

(-infinity, -1) is concave downward

(-1, infinity) is concave upward