Mathematics

Problem

A function

g

is differentiable, increasing and concave upward on the interval

[1,4]

. Let

m_s

be the slope of the secant line through

(1, g(1))

and

(4, g(4))

, and let

m_t

be the slope of the tangent to the curve at some point

c

with

1<c<4

. Which of the following is necessarily true? a)

m_t > m_s

m_t = m_s

c) No definite relation between

m_t

and

m_s

m_t < m_s