Find the absolute extrema of the function on the closed

compagnia04 2021-12-25 Answered
Find the absolute extrema of the function on the closed interval.
y=3x232x, [1, 1]
minimum - ?
maximum - ?
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Expert Answer

John Koga
Answered 2021-12-26 Author has 33 answers
y=3x232x, [1, 1]
Now dydx=2x132
=2x132
=2[1x13]x13
x=0f(0)=0
x=1f(1)=3+2=5
x=1f(1)=32=1
Absolute minimum =(0,0)
Absolute maximum =(1,5)
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Joseph Fair
Answered 2021-12-27 Author has 34 answers
How do you go from setting the derivative of y to a critical point of x=0. Please show those steps. I am getting 1. Thanks
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user_27qwe
Answered 2021-12-30 Author has 230 answers
I was struggling with this too, then after some toil remembered that critical numbers also include where the slope is undefined. The x=1 we kept getting is valid. Though, It is doubled up for evaluation by also being the endpoint on our closed interval. x=0 is where the solution is undefined, which only becomes apparent after combining the fraction!
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