At a critical point of a differentiable function

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

Problem

At a critical point

c

of a differentiable function, if

f'(x)

changes sign from negative to positive as

x

increases through

c

, then

c

is (a) a point of local maximum (b) a point of local minimum (c) a critical point where no conclusion about extremum can be drawn without

f''(c)

(d) a point of inflection with zero slope