Science:Math Exam Resources/Courses/MATH100/December 2011/Question 07/Statement

Full-Solution Problems. In questions 2-8, justify your answers and show all your work. Simplification of answers is not required unless explicitly stated.
Let

$f(x)={\begin{cases}4x-{\frac {\sin ^{2}(2x-2)}{3x-3}}-1,&{\textrm {if}}\;x<1,\\2x+1,&{\textrm {if}}\;x\geq 1.\end{cases}}$

Use the definition of the derivative to find ƒ’(1) or show that ƒ’(1) does not exist.