Does the temperature coefficient of a material depend on temperature? In my textbook, a relationship is plotted between the resistance of the material and the temperature, and the temperature coefficient is defined as the slope of that graph divided by an arbitrary resistance $R_1$ on the graph. Does that mean that the coefficient varies depending on the temperature I choose to divide the slope by?
If so, how does it stand as a valid reference to the material’s resistance growth rate with temperature?
If not, then where did I go wrong with this train of thought?
 A: The temperature coefficient is often defined defined as $\alpha = \dfrac{R_{\rm T}-R_0}{R_0 \, T}$
where the temperatures are in degree Celsius and the reference resistance $R_0$ is measured at $0^\circ \rm C$.  
Which gives the equation $R_{\rm T} = R_0(1 + \alpha\, T)$ ie a linear relationship between resistance and temperature.  
As you have pointed out the relationship is not linear and so a better relationship like $R_{\rm T} = R_0(1 + \alpha\, T + \beta \, T^2 + . . . .)$ can be used for large temperature variations.
This implies that other constants like $\beta$ must be given as well as the temperature coefficient of resistance $\alpha$ as is shown in this reference for a platinum resistance thermometer.
So it does depend on the accuracy to which you are working and the range of temperatures.
If you are given just $\alpha$ with a stated reference temperature then the implication is that as the temperature deviation from the reference temperature increases there will be a corresponding reduction in the accuracy of resistance or temperature as a result of using the first order equation.
A: Yes,temperature coefficient of resistance depends on temperature to some extent. At small temperature changes resistance versus temperature graph is linear which implies temperature coefficient is independent of temperature. At higher temperature the graph is nonlinear which implies temperature coefficient is now not independent of temperature. 
