A differentiable function is continuous on and satisfies with for

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

Problem

A differentiable function

p

is continuous on

[1,7]

and satisfies

p'(4)=0

with

p'(x)\neq 0

for

x\neq 4

. In addition,

p''(4)<0

. Which statement about

p

x=4

is most accurate? (a)

p(4)

is a relative minimum of

p

[1,7]

. (b)

p(4)

is a relative maximum but need not be the absolute maximum on

[1,7]

. (c)

p(4)

is both a relative maximum and the absolute maximum of

p

[1,7]

. (d)

x=4

is an inflection point of

p

[1,7]