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Question #41545

Difficulty: 8/10 | 🟢 Free

The Question

Let $f(x) = x^4 - 6x^3 + 12x^2 - 8x + 3$ . If $L$ is the tangent line to the curve $y = f(x)$ at its point of inflection with the smaller $x$ -coordinate, then the area of the region bounded by the curve $y = f(x)$ and the line $L$ is

Options

A.
$\frac{8}{5}$
B.
$\frac{3}{10}$
C.
$\frac{16}{5}$
D.
$\frac{27}{10}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Specialist

Targeted practice for niche, high-difficulty concepts that frequently appear in JEE Advanced exams.

Concepts Behind This Question

Intersection Point Accuracy|Geometric Interpretation|Point of Inflection Conditions

Why This Question Is Tricky

Common Mistakes

This question tests the geometric interpretation of inflection points and the accurate determination of intersection bounds for area calculation.

A common trap is assuming the area is bounded between the two inflection points (integrating from 1 to 2) or failing to realize that the tangent at an inflection point of a quartic curve has a contact of order 3, meaning it intersects the curve at exactly one other point.

Students who do not solve $f(x) = T(x)$ to find the true upper bound $x=3$ will incorrectly evaluate the integral, often arriving at the trap answer 3/10.

Quick Facts About This Question

Question Information

Subject	Mathematics
Chapter	Application of Integrals - Class 12
Concept	Intersection Point Accuracy
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free