Answer to Question #206764 in Calculus for Shaboo

Question #206764

determine the location and value of the absolute maximum and absolute minimum for the given function. f(x) = (-x+2)⁴ , where 0≤x≤3


1
Expert's answer
2021-06-18T04:39:39-0400


given:

"f(x)=(-x+2)^4,\n\\\\where\\space 0\\le x\\le3"


differentiate with respect to x

"f'(x)=4(-x+2)^3"

now

"f'(x)=0\\\\\\implies-4(-x+2)^3=0\\\\\\implies-x+2=0\\\\\\implies x=2"


now

"f(0)=(0+2)^4=16\\\\f(1)=(-1+2)^4=1\\\\f(2)=(-2+2)^4=0\\\\f(3)=(-3+2)^4=1"


Therefore, the absolute maximum is at x=0 and the value is 16. the absolute minimum is at x=2 and the value is 0


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