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The function f(x)=x^(5)-5x^(4)+5x^(3) ha...

The function `f(x)=x^(5)-5x^(4)+5x^(3)` has

A

One minima and two maxima

B

Two minima and one maxima

C

Two minima and two maxima

D

One minima and one maxima

Text Solution

Verified by Experts

The correct Answer is:
D
`f'(x)=5x^(4)-20x^(3)+15x^(2))`
`f''(x)=20x^(3)-60x^(2)+30x`
`f'(x)=0 rArr x^(2)(x^(2)-4x+3)=0`
`rArr" "x^(2)(x-1)(x-3)=0 rArr x=0, 1, 3`
`f''(1)lt0 and f''(3)=540-540+90 gt0`
`and f''(0)=0 and f'''(0) ne0`
`therefore" Maximum at x = 1 and minimum at x = 3"`
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