For all a, b R the function f (x) = 3x^4 - 4x^3 + 6x^2 + ax + b h… - Vidyadip

MCQ

For all $a, b \in R$ the function $f (x) = 3x^4 - 4x^3 + 6x^2 + ax + b$ has

A
no extremum
✓
exactly one extremum
C
exactly two extremum
D
three extremum .

✓

Answer

Correct option: B.

exactly one extremum

b
$\frac{{dy}}{{dx}}= 12 x (x^2 - x + 1) + a$

$\frac{{{d^2}y}}{{d{x^2}}} = 12 (3x^2 - 2x + 1) > 0 $

$==> \frac{{dy}}{{dx}}$ is an increasing function .

But $\frac{{dy}}{{dx}}$ is a polynomial of degree 3

$==>$ exactly one root

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