Answer to Question #208257 in Statistics and Probability for Muneeb

Question #208257

Determine the location and values of the absolute maximum and absolute minimum for the given function: 𝑓(π‘₯) = (βˆ’π‘₯ + 2) ΰ¬Έ , π‘€β„Žπ‘’π‘Ÿπ‘’ 0 ≀ π‘₯ ≀ 3



1
Expert's answer
2021-06-20T18:26:31-0400

Consider the function "f(x)=(-x+2)^3."

"Df:(-\\infin, \\infin)."

Find the first derivative with respect to "x"


"f'(x)=(-x+2)^3=3(-x+2)^2(-1)"

"=-3(-x+2)^2"

Find the critical number(s):


"f'(x)=0=>-3(-x+2)^2=0"

"x=2"

Critical number: "2."

If "0\\leq x\\leq 3"


"f(0)=(-0+2)^3=8"

"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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