The temperature at the point $( x , y )$ on the square with vertices (0, 0), (0, 1), (1, 0) and (1, 1) is given by $T ( x , y ) = 4 x ^ { 2 } + 8 y ^ { 2 }$
Find the hottest and coldest points on the square.

A)(2, 2), (0, 0)
B) (0, 1), (0, 0)
C) (1, 1), (1, 0)
D) (1, 0), (0, 0)
E) (1, 1), (0, 0)

Question

The temperature at the point $( x , y )$ on the square with vertices (0, 0), (0, 1), (1, 0) and (1, 1) is given by   $T ( x , y ) = 4 x ^ { 2 } + 8 y ^ { 2 }$  
Find the hottest and coldest points on the square.
 
A)(2, 2), (0, 0)
B) (0, 1), (0, 0)
C) (1, 1), (1, 0)
D) (1, 0), (0, 0)
E) (1, 1), (0, 0)

Quizplus · Accepted Answer

The temperature function $T(x, y) = 4x^2 + 8y^2$ increases as $x$ and $y$ increase because both squared terms are multiplied by positive coefficients. Therefore, the hottest point is at the maximum values of $x$ and $y$ within the square, which is (1, 1). The coldest point is at the minimum values of $x$ and $y$, which is (0, 0), where the temperature function yields the smallest value.

The Temperature at the Point (x,y)( x , y )(x,y) On the Square with Vertices (0, 0), (0, 1), (1

The Temperature at the Point $( x , y )$ On the Square with Vertices (0, 0), (0, 1), (1