Answer to Question #253508 in Calculus for Roger

Question

In the temperature range between 0 degrees * C and 700 ^ 0 * 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 7 is the temperature in degrees Celsius. Where in the interval from 0 °C to 700 ^ 0 * C is the resistance of the thermometer most sensitive and least sensitive to temperature changes? [/lint: Consider the size of dR / d * T in the interval 0 <= T <= 700.1

Answer 1

$$R=10+0.04124T-1.779\times 10^{-5}T^2$$

$$\dfrac{dR}{dT}=0.04124-3.558\times10^{-5}T$$

The function $\dfrac{dR}{dT}$ decreases for $T\in[0\degree C, 700\degree C].$

$$\dfrac{dR}{dT}|_{T=0\degree C}=0.04124\ \Omega /\degree C$$

$$\dfrac{dR}{dT}|_{T=700\degree C}=0.016334\ \Omega /\degree C$$

The resistance is most sensitive to temperature changes at $T=0\degree C,$ least sensitive at $T=700\degree C.$