Which of the following represents the interval where f (x) = xe^x is concave up?

Question

a. x < -2

b. x < -1

c. -2 < x < -1

d. x > -2

e. x > -1

Answer 1

f^'(x) = e^x + xe^x

f^"(x) = e^x + e^x + xe^x = e^x (2 + x)

e^x > 0 for all x, and (2 + x) > 0 for x > - 2

x > - 2