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Question

Examine the function f(x)=x+25x for maxima and minima

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Solution

f(x)=x+25x
Taking derivative on both sides,
f(x)=125x2 ---- ( 1 )
Critical point :
f(x)=0
125x2=0
x225=0
x2=25
x=±5
Now, taking derivative of ( 1 ), we get
f′′(x)=50x3
Now, f′′(5)=50(5)3=25
f′′(5)=50(5)3=25
Maximum value of f(x):f(5)=25
Minimum value of f(x):f(5)=25

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