# Differentiable Functions

• Apr 24th 2010, 03:35 AM
acevipa
Differentiable Functions
Could someone help me with this question:

$\displaystyle The\ function\ is\ given\ by$

$\displaystyle f(x)=x\ for\ 0 \leq x<1$
$\displaystyle f(x)=1/x^2\ for\ 1 \leq x<2$

$\displaystyle and\ f(x)=f(x+2)\ for\ all\ x$

$\displaystyle 1)\ Is\ f(x)\ odd,\ even\ or\ neither.\ Explain?$

$\displaystyle 2)\ Is\ f(x)\ periodic?\ If\ so\ state\ the\ period.$

$\displaystyle 3)\ Find\ any\ relevant\ maxima\ or\ minima\ of\ f(x)$
• Apr 24th 2010, 04:45 AM
schmeling
odd and even functions have the following properties:

even F(x)=F(-x)

odd -F(x)=F(-x)

the first function in your question is odd, the second is even. Using these fomrulas you can work it out by yourself quite easily.

a function is periodic when its values repeat itself every now and then. Therefore if we have a function that looks like

F(x)=F(x+P) it is most certainly a periodic function. P is the period.

finally minima and maxima. You can see that differentiating these functions will not help here. You do know the limits though and you can easily find for which value the function will have its largest and smallest value.