The function is differentiable for all

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The function q(x)=∣2x−3∣3q(x)=|2x-3|^{3} is differentiable for all x≠32x\neq\dfrac{3}{2}. Which of the following gives q′(x)q'(x) for x≠32x\neq\dfrac{3}{2}? (a) q′(x)={6(2x−3)2,x<32−6(2x−3)2,x>32q'(x)=\begin{cases}6(2x-3)^{2}, & x<\dfrac{3}{2}\\ -6(2x-3)^{2}, & x>\dfrac{3}{2}\end{cases} (b) q′(x)=6(2x−3)2 for all x≠32q'(x)=6(2x-3)^{2}\text{ for all }x\neq\dfrac{3}{2} (c) q′(x)={−6(2x−3)2,x<326(2x−3)2,x>32q'(x)=\begin{cases}-6(2x-3)^{2}, & x<\dfrac{3}{2}\\ 6(2x-3)^{2}, & x>\dfrac{3}{2}\end{cases} (d) q′(x)={−3(2x−3)2,x<323(2x−3)2,x>32q'(x)=\begin{cases}-3(2x-3)^{2}, & x<\dfrac{3}{2}\\ 3(2x-3)^{2}, & x>\dfrac{3}{2}\end{cases}

Related theory

Browse the problem library