Consider the function on the interval

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

Problem

Consider the function

g(x)=\dfrac{x^{2}}{2}-\sin x

on the interval

[0,4]

. Which statement correctly describes the absolute extrema of

g

on this interval? (a)

g

attains its absolute maximum at the unique critical point

c

(0,4)

. (b)

g

attains its absolute minimum at

x=0

and its absolute maximum at

x=4

. (c)

g

attains its absolute minimum at the unique critical point

c

(0,4)

. (d)

g

attains its absolute minimum at both endpoints

x=0

and

x=4