Mathematics

Problem

The function

q(x)=|2x-3|^{3}

is differentiable for all

x\neq\dfrac{3}{2}

. Which of the following gives

q'(x)

for

x\neq\dfrac{3}{2}

? a)

q'(x)=\begin{cases}6(2x-3)^{2}, & x<\dfrac{3}{2}\\ -6(2x-3)^{2}, & x>\dfrac{3}{2}\end{cases}

q'(x)=6(2x-3)^{2}\text{ for all }x\neq\dfrac{3}{2}

q'(x)=\begin{cases}-6(2x-3)^{2}, & x<\dfrac{3}{2}\\ 6(2x-3)^{2}, & x>\dfrac{3}{2}\end{cases}

q'(x)=\begin{cases}-3(2x-3)^{2}, & x<\dfrac{3}{2}\\ 3(2x-3)^{2}, & x>\dfrac{3}{2}\end{cases}