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Let f(x)=(x-1)^(4)(x-2)^(n), n in N.. Th...

Let `f(x)=(x-1)^(4)(x-2)^(n)`, n in N.. Then f(x) has

A

a local maximum at x=1 if n is odd

B

a local maximum at x=1 if n is even

C

a local minimum at x=2 if n is even

D

a local maximum at x=2 if n is odd

Text Solution

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The correct Answer is:
A, D
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Knowledge Check

  • Let f(x)=(x-1)^(4)(x-2)^(n) , n inN . Then f(x) has

    A
    a maximum at x= 1 if n is odd
    B
    a maximum at x=1 if n is even
    C
    a minimum at x=1 if is even
    D
    a minima at x=2 if n is even

  • f(x)=(x-2)^(2)x^(n), n inN then f(x) has

    A
    maximum at `x=2AAn in N`
    B
    minimum at x=2 if n is even only
    C
    maximum at x=0 if is even
    D
    minimum at x=0 if n is even and minimum at `x=2 AA n inN`

  • If a polynomial of degree 'n' satisfies f(x)= f'(x) f^(11) (x) AA n in R " then " f(x) is

    A
    an onto function
    B
    an into function
    C
    no such function is possible
    D
    even function

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