Science:Math Exam Resources/Courses/MATH100/December 2010/Question 04 (d)/Statement

Full-Solution Problems. In questions 2-8, justify your answers and show all your work. If a box is provided, write your final answer there. Simplification of answers is not required unless explicitly requested.

Let

$f(x)={\begin{cases}{\frac {4}{\pi }}\tan ^{-1}x&{\text{if }}x\geq 1\\2-x^{4}&{\text{if }}x<1\end{cases}}$

NOTE: Another notation for tan^-1(x) is arctan(x)

Determine open intervals where the graph of ƒ is concave upwards or concave downwards, and the x-coordinates of all inflection points (if any).