Let be twice differentiable

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let

f

be twice differentiable, and suppose

f'(c)=0

and

f''(c)>0

. Which of the following statements best describes the behavior of

f

x=c

? (a)

f

has a local maximum at

x=c

. (b)

\text{No conclusion about local extrema can be drawn from this information.}

(c)

f

has a local minimum at

x=c

. (d)

x=c

is a point of inflection of

f