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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 Cx=a is not a point of maximum or minimum f(x)=(x−a)2n(x−b)2m+1 f′(x)=(2m+1)(x−a)2n(x−b)2m+2n(x−a)2n−1(x−b)2m+1 For maxima or minima, f′(x)=0 ⇒x=a,b f′′(x)=2m(2m+1)(x−a)2n(x−b)2m−1+2n(2m+1)(x−a)2n−1(x−b)2m+2n(2n−1)(x−a)2n−2(x−b)2m+1