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

$f(x)=\{\begin{array}{ll}4x-\frac{{\sin }^2(2x-2)}{3x-3}-1,& \text{if}x<1,\\ 2x+1,& \text{if}x\ge 1.\end{array}$

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