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Question

If f(x)=(xa)2n(xb)2m+1 where m.n N, then

A
x=a is a point of minimum
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B
x=a is a point of maximum
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C
x=a is not a point of maximum or minimum
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D
No value of k satisfies the requirement
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Solution

The correct option is C x=a is not a point of maximum or minimum
f(x)=(xa)2n(xb)2m+1
f(x)=(2m+1)(xa)2n(xb)2m+2n(xa)2n1(xb)2m+1
For maxima or minima,
f(x)=0
x=a,b
f′′(x)=2m(2m+1)(xa)2n(xb)2m1+2n(2m+1)(xa)2n1(xb)2m+2n(2n1)(xa)2n2(xb)2m+1
+2n(2m+1)(xa)2n1(xb)2m
f′′(x)=0 at x=a

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