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Let f(x)=x^4-4x^3+6x^2-4x+1. Then, (a) f...

Let `f(x)=x^4-4x^3+6x^2-4x+1.` Then, (a) `f` increase on `[1,oo]` (b) `f` decreases on `[1,oo]` (c)`f` has a minimum at `x=1` (d)`f` has neither maximum nor minimum

A

f increases on `[1,oo]`

B

f decreases on `[1,oo]`

C

f has a minimum at x=1

D

f has neither maximum nor minimum

Text Solution

Verified by Experts

The correct Answer is:
1,3
f(x)=`4(x^(3)=3x^(2)+3x-1)=4(x-1)^(3)gt0 for x gt1`
Hence f increases in `[1,oo)` Moreover f(x)`lt0 for x lt 1`
Hence f has a minimum at x =1
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