The function x^5 - 5 x^4 + 5 x^3 - 1 is - Vidyadip

MCQ

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

A
Maximum at $x = 3$ and minimum at $x = 1$
B
Minimum at $x = 1$
✓
Neither maximum nor minimum at $x = 0$
D
Maximum at $x = 0$

✓

Answer

Correct option: C.

Neither maximum nor minimum at $x = 0$

c
(c) Let $f(x) = {x^5} - 5{x^4} + 5{x^3} - 1$

==> $f'(x) = 5{x^4} - 20{x^3} + 15{x^2} = 0$

$\therefore (x - 3)(x - 1) = 0$ or $x = 3,1$

Now $f''(x) = 20{x^3} - 60{x^2} + 30x$

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 $x = 0$.

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