A function is differentiable

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

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

(b)

m_t = m_s

m_t

and

m_s

(d)

m_t < m_s