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??
ok, so let me re-try this:
a) point of inflection (0,8)
concave up when x>0
concave down when x<0
b) no local max or min points
is this correct now?
and another question on a side note: when a function has a vertical tangent, that means that the function can still have concavity, right?