Let be continuous on and differentiable on with for all in

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

Problem

Let

g

be continuous on

[0,5]

and differentiable on

(0,5)

with

g'(x)\ge 2

for all

x

(0,5)

. Which of the following must be true on the interval

(0,5)

? (a) There exists

c

(0,5)

such that

g'(c)=2

. (b) The equation

g(x)=7

has at most one real solution. (c) The equation

g(x)=7

has at least one real solution. (d) There exists

c

(0,5)

such that

g'(c)=0