Determine the location and values of the absolute maximum and absolute minimum for the given function: π(π₯) = (βπ₯ + 2) ΰ¬Έ , π€βπππ 0 β€ π₯ β€ 3
Consider the function "f(x)=(-x+2)^3."
"Df:(-\\infin, \\infin)."
Find the first derivative with respect to "x"
"=-3(-x+2)^2"
Find the critical number(s):
"x=2"
Critical number: "2."
If "0\\leq x\\leq 3"
"f(3)=(-3+2)^3=-1"
"f(2)=(-2+2)^3=0"
The function "f(x)" has the absolute maximum with value of "8" on "[0,3]" at "x=0."
The function "f(x)" has the absolute minimum with value of "-1" on "[0,3]" at "x=3."
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