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(Steps Shown) In the temperature range between 0^circ C and 700^circ C the resistance $R[$ in ohms (Ω)] of a certain platinum resistance thermometer is

Question: In the temperature range between \(0^{\circ} \mathrm{C}\) and \(700^{\circ} \mathrm{C}\) the resistance $R[$ in ohms \((\Omega)]\) of a certain platinum resistance thermometer is given by

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

where \(T\) is the temperature in degrees Celsius. Where in the interval from \(0^{\circ} \mathrm{C}\) to \(700^{\circ} \mathrm{C}\) is the resistance of the thermometer most sensitive and least sensitive to temperature changes? [Hint: Consider the size of \(d R / d T\) in the interval \(0 \leq T \leq 700 .]\)

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