Answer to Question #252400 in Calculus for Steve

Question

In the temperature range between 0°C and 700°C the resistance R [in ohms] of a certain platinum resistance thermometer is given by

R = 10 + 0.04124T − 1.779 × 10^(−5)T^2

where T is the temperature in degrees Celsius. Where in the interval from 0°C to 700°C is the resistance of the thermometer most sensitive and least sensitive to temperature changes? [Hint: Consider the size of dR/dT in the interval 0 ≤ T ≤ 700.].

Answer 1

As we know the resistance would be sensitive for we need to find:

$\cfrac{dR}{dT}$

so from here we find that :

$\cfrac{d}{dT}(10 + 0.04124T − 1.779 × 10^{−5}T^2)$

$0.04124-2\times1.779\times10^{-5}T$

Now it is clear that the $\cfrac{dR}{dT}$ is decreasing

Now the Resistance would be most sensitive when :

$\cfrac{dR}{dT}$ is 0,, so for here that would be

$T=1159.07 \ \ ^oC$

it would be least sensitive for :

$\cfrac{dR}{dT}$ is minimum

and for the given range it would be for :

$T= 700 \ \ ^oC$