The function is continuous on and differentiable on

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

Problem

The function

h

is continuous on

[0,6]

and differentiable on

(0,6)

. It is known that •

h'(x)>0

for

0<x<2

, •

h'(x)<0

for

2<x<4

, •

h'(x)>0

for

4<x<6

, and

h(0)=1

h(2)=5

h(4)=2

h(6)=3

. Which statement correctly identifies the absolute minimum of

h

[0,6]

? (a) It occurs at

x=4

because

h'(x)

changes from negative to positive there. (b) It occurs at

x=6

because

h

is increasing on

(4,6)

. (c) It occurs at

x=0

because

h(0)

is less than the function values at all other candidates. (d) It occurs at

x=4

because

h(4)

is less than the function values at

x=2

and

x=6