The temperature of points in space given by a scalar field is

$T(x,y,z)=x^2+y^2-z$

a$.$ Find the temperature, $T,$ at the point $(-1,0,5).$

b$.$ Evaluate the directional derivative of the scalar function $T(x,y,z)$ at the point $(1,3,-1$ in the direction of $(2,1,2).$

c$.$ An isothermal is a surface upon which the temperature of the surface is constant

i$.$ find the equation of the isothermal $($i$.$e$.$ the surface$)$ through the point $(1,1,2)$ by making $z$ the subject

ii$.$ in Matlab plot the equation of the isothermal contours in the $x-y$ plane s$.$t$.-5x5$ and $-5y5($include screenshot$)$

d$.$ A mosquito is located at the point $(1,1,2),$ and desires to fly in such a direction that it will get cool as soon as possible. In what direction should it move and why?