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Question #40972

Difficulty: 8/10 | 🟢 Free

The Question

Let $f(x) = |2x^3 - 9x^2 + 12x - 3|$ . If $M$ and $m$ are the global maximum and global minimum values of $f(x)$ on the interval $[0, 3]$ respectively, then the value of $M + m$ is

Options

A.
$6$
B.
$7$
C.
$9$
D.
$3$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Bridge

Practice problems that bridge the gap between foundational theory and advanced practical application.

Concepts Behind This Question

Range and Coefficient of Range|Global Extrema on Intervals|Modulus Function Breakdown

Why This Question Is Tricky

Common Mistakes

The question tests the student's ability to find the global extrema of a modulus function on a closed interval.

The primary trap is 'Modulus Folding'.

Students often evaluate the absolute value of the function at critical points and endpoints, obtaining $|-3|=3$ , $|2|=2$ , $|1|=1$ , and $|6|=6$ , and incorrectly conclude that the minimum is $1$ .

They fail to recognize that because the original function $g(x)$ changes sign (from $-3$ to $2$ ), it must pass through $0$ , making the true minimum of $|g(x)|$ equal to $0$ .

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Statistics - Class 11
Concept	Range and Coefficient of Range
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free