NIMCET 2014 Question Paper with solutions

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Question : 26 of 120

Marks: +1, -0

A condition that

x^2 +ax^2 + bx + c

may have no extremum is

$a^2$ ≥ 3b
$b^2$ < 3a
$a^2$ < 3b
$b^2$ ≥ 3a

Solution:

We have
f (x) =

x^3+ax^2

+ bx + c
f'(x) =

3x^2

+ 2ax + b
Condition for no extremum

b^2

- 4ac < 0
⇒

4a^2

- 4 × 3b < 0
⇒

a^2

- 3b < 0
⇒

a^2

< 3b

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