Inflection points (Calc problem)?

Question

Find the inflection point(s), if any, of the function:

f(x) = 3x e^x.

Show that the function f(x) = x^3 + x - 1 is increasing for all x.

Thanks for the help in advance!!!!

Answer 1

1) f(x) = 3xe^x
f '(x) = 3(xe^x + e^x)
f ''(x) = 3(xe^x + e^x + e^2) = 3(xe^x + 2e^x) = 0
xe^x = -2e^x
x = -2

2) f(x) = x^3 + x -1
f '(x0 = 3x^2 + 1 is positive for all x

Answer 2

perchance you haven't any longer differentiated properly as to the 2nd area of the question if the 2nd derivative equation is under 0 you have a maxima, extra suitable than 0 you have a minima and equivalent to 0 you have a component of inflection