The function $x^{5} - 5 x^{4} + 5 x^{3} - 1$ is

Maximum at and minimum at x=1

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Minimum at x =1

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Neither maximum nor minimum at x=0

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Maximum at x =0

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Solution

The correct option is C Neither maximum nor minimum at x=0
Let $f (x) = x^{5} - 5 x^{4} + 5 x^{3} - 1$
$\Rightarrow f^{'} (x) = 5 x^{4} - 20 x^{3} + 15 x^{2} = 0$
$∴ (x - 3) (x - 1) = 0$ , x =0,3,1
Now $f^{''} (x) = 20 x^{3} - 60 x^{2} + 30 x$
Put x=3 and 1, we get f"(3) =+ve and f"(1) =-ve and f"(0) =0.Hence f(x) neither maximum nor minimum at x=0.

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The function x5−5x4+5x3−1 is

The correct option is C Neither maximum nor minimum at x=0Let f(x)=x5−5x4+5x3−1 ⇒f′(x)=5x4−20x3+15x2=0 ∴(x−3)(x−1)=0 , x =0,3,1 Now f′′(x)=20x3−60x2+30x Put x=3 and 1, we get f"(3) =+ve and f"(1) =-ve and f"(0) =0.Hence f(x) neither maximum nor minimum at x=0.

The function $x^{5} - 5 x^{4} + 5 x^{3} - 1$ is