QPaperGen
Authenticated
Generate
Q-Bank
MCQ Test
Login
ID:
Class: 12
Subject: Math
Topic: Application of Derivative
Type: Mcq
Year: 2025
Question:
The function \(f(x)=x^{2}-4x+6\) is increasing in the interval
A.
\((0, 2)\)
B.
\((-\infty, 2]\)
C.
\([1, 2]\)
D.
\([2, \infty)\)
Official Solution
Correct Answer:
\([2, \infty)\)
Explanation:
\[f(x) = x^2 - 4x + 6\]
\[f'(x) = 2x - 4\]
For Critical Point set \(f'(x) = 0\) implies \[2x - 4 = 0 \implies 2x = 4 \implies x = 2\]
The function is increasing when \(f'(x) > 0\) implies \[2x - 4 > 0\]\[2x > 4\]\[\mathbf{x > 2}\]
AI Teacher
Disclaimer:
AI-generated content may contain errors. Please verify with standard textbooks.