Let . At , one has and . Which of the following best describes the point…

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

Problem

Let

p(x)=x^{4}

. At

x=0

, one has

p'(0)=0

and

p''(0)=0

. Which of the following best describes the point

x=0

? (a)

x=0

is neither a local maximum nor a local minimum because

p''(0)=0

. (b)

x=0

is a local maximum because

p'(x)

changes from positive to negative at

x=0

. (c)

x=0

is a local minimum because

p'(x)

changes from negative to positive at

x=0

. (d)

x=0

is an inflection point because

p''(0)=0