Consider the function

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

h(x)=x^{2/3}(2-x)

, defined for all real

x

. At

x=0

, the derivative

h'(x)

is undefined, but

x=0

is still a critical point. Which statement accurately describes the behavior of

h

x=0

? (a)

x=0

is neither a local extremum nor a point of inflection because

h'(0)

does not exist. (b)

x=0

is a local minimum since

h(x)>h(0)

for all

x

sufficiently close to

0

except

x=0

. (c)

x=0

is a point of inflection because the concavity of

h

changes at

x=0

. (d)

x=0

is a global minimum because

h(x)\ge 0

for all real

x

and

h(0)=0