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Answer on Calculus Question for hsd

Question #17672
Find the absolute maximum and minimum values of the following function on the given interval. If there are multiple points in a single category list the points in increasing order in x value and enter N in any blank that you don't need to use.

f(x)=8e^(−x)−8e^(−2x) , [0,1]

Absolute maxima
x = y =
x = y =
x = y =

Absolute minima
x = y =
x = y =
x = y =
Expert's answer
we can check only ends of interval and points where f'=0
e^(-x)>0 so

x=0 f(x)=8-8=0
x=ln(2) f(x)=8e^(-ln(2))-8e^(-ln(4))=4-2=2
x=1 f(x)=8(1/e-1/e^2)
absolute minima x=0 y=0
absolute maxima x=ln(2) y=2

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