Question

Determine the concavity of the function if f(x)=x^(1/3) * (x-4)

Answer 1

Find the second derivative: \[\frac{d^2f}{dx^2}\]
And set it to zero. Find the inflection points (where it switches concavity). Then test values on either side to see if it is positive or negative. If it is positive, concave up; if it is negative, concave down.