Answer
$T=0°C$ -> most sensitive
$T=700°C$ -> least sensitive
Work Step by Step
$R=10+0.04124T-1.779\times10^{-5}T^2$
Derivating with respect to $T$:
$\frac{dR}{dT}=0.04124-3.558\times10^{-5}T$
It's a line function. The most and least sensitive to temperature changes occurs at the maximum and minimum (respectively) value of the module of derivative (the sign will only tell you if the change is to a greater or lower $R$).
At the borders of the interval:
$T=0$ gives $\frac{dR}{dT}=0.04124$
$T=700$ gives $\frac{dR}{dT}=0.016334$
Since the function is linear, any other value of $T$ located in $0\leq T \leq700$ will give values between those values of $\frac{dR}{dT}$.
So
$T=0°C$ -> most sensitive
$T=700°C$ -> least sensitive
