A function is matched below against an interval where it is suppo… - Vidyadip

MCQ

A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched

Interval Function

✓
$\left( { - \infty ,\,{1 \over 3}} \right]$ $3{x^2} - 2x + 1$
B
$(-\infty, -4]$ ${x^3} + 6{x^2} + 6$
C
$(-\infty, \infty)$ ${x^3} - 3{x^2} + 3x + 3$
D
$[2, \infty)$ $2{x^3} - 3{x^2} - 12x + 6$

✓

Answer

Correct option: A.

$\left( { - \infty ,\,{1 \over 3}} \right]$ $3{x^2} - 2x + 1$

a
(a) $f(x) = 3{x^2} - 2x + 1$,$f'(x) = 6x - 2 \ge 0$ ==> $x \ge \frac{1}{3}$

Option $ (a) $ is incorrect.

Checking other function similarly we find that they are correctly matched.

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