Find the points of inflection of the graph of the function. (If an answer does not exist, enter DNE.)

Question

f(x) = 1/3x^4 + 4x^3

for some reason I am not getting the right answer; I got the graph on my calculator but it seems weird.

Answer 1

4/3x^3 + 12x^2 = f'(x)
4/3x^3 + 12x^2 =0
multiply by 3 to clear fractions
4x^3 + 36x^2 =0
factor out 4x^2
(4x^2)(x+9)=0
x = 0, x =-9 are critical numbers
f'(-10)= -,f'(-8) = +, f'(1) = +
(-9,-729) is an inflection, actually a minimum point

Answer 2

Thanks for the help but I am still confused because it's asking for

smaller x-value
larger x-value

so what would that be?