find the absolute extrema of the function on the closed interval.\n$f(x)=8 - x$, $-2,4$\nminimum…

find the absolute extrema of the function on the closed interval.\n$f(x)=8 - x$, $-2,4$\nminimum $(x,y)=(quad)$\nmaximum $(x,y)=(quad)$

find the absolute extrema of the function on the closed interval.\n$f(x)=8 - x$, $-2,4$\nminimum $(x,y)=(quad)$\nmaximum $(x,y)=(quad)$

Answer

Explanation:

Step1: Find the derivative of the function

The derivative of (f(x)=8 - x) is (f^\prime(x)=-1). Since (f^\prime(x)) is never zero (it is a constant non - zero value), there are no critical points in the open interval ((-2,4)).

Step2: Evaluate the function at the endpoints of the interval

  • When (x=-2): (y = f(-2)=8-(-2)=8 + 2=10)
  • When (x = 4): (y=f(4)=8-4=4)

Answer:

minimum ((x,y)=(4,4)) maximum ((x,y)=(-2,10))