Let be continuous on and differentiable on

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

g

be continuous on

[2,8]

and differentiable on

(2,8)

. Suppose

g'(x)=0

only at

x=5

, and

g''(5)>0

. Explain briefly why

x=5

is where

g

attains its absolute minimum on

[2,8]