Consider the function f(x)= cases x, & x 0 x^ 2 , & 0<x<2 4, & x 2

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

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