Suppose that the temperature at a point (x,y), on a metal plate is $T(x,y)=4x^2-4xy+y^2$, An ant, walking on the plate, traverses a circle of radius 5 centered at the origin. What is the highest temperature encountered by the ant?

A particle is at rest at the origin. It moves along the x −axis with an acceleration $x-x^2$ , where x is the distance of the particle at time t. The particle next comes to rest after it has covered a distance

Consider the function  $$f(x)=\begin{cases}{-{x}^3+3{x}^2+1,} & {if\, x\leq2} \\ {\cos x,} & {if\, 2{\lt}x\leq4} \\ {{e}^{-x},} & {if\, x{\gt}4}\end{cases}$$   Which of the following statements about f(x) is true:

The function $f(x)=\frac{x}{1+x\tan x}$ , $0\leq x\leq\frac{\pi}{2}$ is maximum when 

The maximum value of 4 sin² x + 3 cos² x + sin(x/2) + cos(x/2) is

The critical point and nature for the function f(x, y) = x² –2x + 2y² + 4y – 2 is

If  , then x = 0 is