a)Determine the concavity and points of inflection.

b) Find the local max and local min points.

Can someone check my work?

f(x)=8-x^(1/3)

f'(x)=-1/(3^(2/3))

f'(x)= undefined when x=0

(0,8)

f''(x)=2/(9x^(5/3))

f''(x)=undefined when x=0

(0,8)

therefore point of inflection occurs at (0,8) and there is no concavity, no local max and min points.

Question: for this particular case, a vertical tangent, there is no concavity correct??