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Question

Find the greatest and the least values of the following functions.
y=x5x3+x+2 on the interval [-1, 1].

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Solution

y=x5x3+x+2
dydx=5x43x2+1=0
5x43x2+1=0,has imaginary roots, ,hence there is no absolute maximum for this function.
f(1)=1 is the local minimum in the interval [1,1]
f(1)=3 is the local maximum in the interval [1,1]

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