Mathematics

Mathematics

Problem

The piecewise-defined function

h

has a graph consisting of two line segments:

h(x)=\begin{cases}-2x+6,&0\le x<3,\\ x-3,&3\le x\le5.\end{cases}

Which statement about the first derivative

h'

is true? a)

h'=-2

for

0<x<3

,

h'=0

at

x=3

, and

h'=1

for

3<x<5

. b)

h'=-2

for

0<x<3

,

h'=1

at

x=3

, and

h'=1

for

3<x<5

. c)

h'=-2

for

0<x<3

,

h'

is undefined at

x=3

, and

h'=1

for

3<x<5

. d)

h'=-2

for

0<x<3

,

h'=-2

at

x=3

, and

h'=1

for

3<x<5

.

Browse the problem library