At a critical point of a twice differentiable function

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

Problem

At a critical point

x=c

of a twice differentiable function

f

, it is given that

f'(c)=0

and

f''(c)<0

. Which of the following statements is correct about

x=c

? (a) The nature of

x=c

cannot be determined from the given data (b)

f(c)

is a local minimum (c)

f(c)

is a local maximum (d)

x=c

is a point of inflection