Question

Suppose that the temperature $T$at every point $(x,y)$ in the plane cartesian is given by the formula $T=1-x^2+2y^2$
The correct statement about the maximum and minimum temperature along the line $x+y=1,$ is

• A. Minimum is$-1$ There is no maximum.
• B. Maximum is $-1$ There is no minimum
• C. Maximum is $0$ Minimum is $-1$
• D. There is neither a maximum nor a minimum along the line

Answer 1

The correct option is A Minimum is$-1$ There is no maximum.

$T=1-x^2+2y^2$ where $x+y=1$
$T=1-x^2+2(1-x{)}^2$
$T=1-x^2+2(1+x^2-2x)$
$T=x^2-4x+3=(x-2{)}^2-1$
$T_{max}=$ doesn't exist
$T_{min}=-1$
Hence,$\left(a\right)$ is the correct answer.