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Question

Find the values at which max. and min. value of the following exist.
x55x4+5x310.

A
max=0,min=1
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B
max=0,min=3
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C
max=1,min=0
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D
max=1,min=3
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Solution

The correct option is D max=1,min=3
y=x55x4+5x310
dydx=5x2(x24x+3)
dydx=5x2(x1)(x3)=0 for min. or max
x=0,1,3.
Now d2ydx2=20x360x2+30x=10x(2x26x+3)
So at x=0, d2ydx2=0, Hence point x=0 is neither maxima nor minima.
and (d2ydx2)x=1<0 and (d2ydx2)x=3>0
Thus point x=1 is maxima and x=3 is minima
ymax=9 and ymin=37

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