Mathematics

Mathematics

Problem

Consider the function

f(x)=\begin{cases}\sin x, & x\le 0\\ x^{2}, & 0<x<2\\ 4, & x\ge 2.\end{cases}

Which of the following gives

f'(x)

for all real numbers

x

? a)

f'(x)=\sin x

for

x<0

,

2x

for

0<x<2

, and

0

for

x>2

b)

f'(x)=\cos x

for

x<0

,

2x

for

0<x<2

, and

0

for

x>2

c)

f'(x)=\cos x

for

x<0

,

2x

for

0\le x\le 2

, and

0

for

x>2

d)

f'(x)=\cos x

for

x<0

,

2x

for

0<x<2

, and

4

for

x>2

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