Problem #$4$: The temperature $at$ a point $(x,y)on$ a rectangular metal plate $is$ given $by$

$T(x,y)=\frac{100}{3x^2+y^2}$

$(a)$ Find the rate $of$ change $ofTat$ the point $(5,6)in$ the direction $of$ the vector $(-3,-4)$

$(b)At$ the point $(5,6),$ find a unit vector $in$ the direction $in$ which the temperature increases the fastest.

$(c)$ What $is$ the maximum rate $of$ change $ofTat$ the point $(5,6)?$

Problem #$4(a)$:

Round your answer $to4$ decimals.

Problem #$4(b)$: $-\frac{3000}{3232},-\frac{1200}{3232}$

Enter your answer

symbolically, $asin$ these

examples

Enter the components $of$ the unit vector

separated with a comma.

$-\frac{3000}{3232},-\frac{1200}{3232}$

Round your answer $to4$ decimals.

Problem #$4(c)$:

Submit Problem #$4$ for Grading