# Given the function #f(x)= 1/12x^4 + 1/6x^3-3x^2-2x+1# how do you find any points of inflection and determine where the curve is concave up or down?

##### 1 Answer

If

So

Now we notice that the third derivative:

(this does make sense since we know how the graphic of a quartic polynomial behave)

Now, if the function is twice differentiable, the concavity is determined by the sign of its second derivative:

So in U the curve is concave up, and in D the curve is concave down