Locate all inflection points of
f(x) = x^4 + 6 x^3 - 24x^2 + 26
a) show 2nd derivative
b)show inflections point(s) and explain in complete sentences why these numbers are inflection points and not critical points.

Question

Locate all inflection points of 
f(x) = x^4 + 6 x^3 - 24x^2 + 26
a) show 2nd derivative
b)show inflections point(s) and explain in complete sentences why these numbers are inflection points and not critical points.

anonymous · Answer

1st derivative I have : 4x^3 + 18x^2 - 48
2nd derivative I have 12x^2 + 36x - 48
I get inflection points of  x=1  x=-4
The points x=1  and x=-4 are inflection points because this is where the concavity changes. These points are not critical points because ....? (not sure what to put) HELP

anonymous · Answer

right

anonymous · Answer

But what can I put to say why it is not a critical point

anonymous · Answer

should it be -48x?