The function has a critical number at

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

The function

h(x)=x^{5}-5x^{3}

has a critical number at

x=0

. Which statement best describes this point? (a)

x=0

is a local maximum because

h'(x)

changes from positive to negative at that point. (b)

x=0

is a local minimum because

h''(0)>0

. (c)

x=0

is a point of inflection because

h''(0)=0

and

h'

does not change sign there. (d) The nature of

x=0

cannot be determined without evaluating higher–order derivatives such as

h^{(4)}(0)