Identifying Points of Inflection for a Polynomial Function

[hcarter50]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

Found f'(x)= x^2(4/3x+12)
Also found critical numbers to x=0 and x=-9

I don't know how to get point of inflection

 

[Dick]

Points of inflection are where the function changes concavity. They are related to second derivatives, aren't they? Look it up.

 

[ankitp4t3l]

For inflection points:
Find the second derivative of the function and set it equal to zero.

I found that that x=-6 and x=0.

Test some points right and left of the second derivative zeros (^) to confirm concave up or concave down. A positive value is concave up, vice versa :)