Ben Blakesley, Researcher at King’s College London, Numerade Educator

03:51

Calculus 3

Let f be a continuous real-valued function defined
on [a,b] and let f be differentiable on
(a,b).
Mark all of the following statements
that
are necessarily true:
a. f has its maximum and minimum in the interior
of [a,b]
b. f has its maximum and minimum
on [a,b]
c. f has at least one critical point on
(a,b)
d. if x in (a,b) is a critical point
of f then x is a point of minimum
or maximum of f
e. if x in (a,b) is a point of minimum
or maximum of f then x is a
critical point of f