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Joint Entrance Examination
Mathematics
Application of Derivatives
Question 80
Question 80 of 212
Medium
MCQ
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
A
Interval Function (- \[\infty \], \[\infty \]) x3 - 3x2 + 3x + 3
B
Interval Function [2, \[\infty \]) 2x3 - 3x2 - 12x + 6
C
Interval Function \[\left( { - \infty ,{1 \over 3}} \right]\] 3x2 - 2x + 1
D
Interval Function (\[ - \infty \], - 4 ) x3 + 6x2 + 6
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Official solution
Clearly function \[f\left( x \right) = 3{x^2} - 2x + 1\] is increasing when \[f'\left( x \right) = 6x - 2 \ge 0 \Rightarrow \,\,\,\,\,x \in \left[ {1/3,\left. \infty \right)} \right.\] \[\therefore\]
f
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f(x)
f
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is incorrectly matched with \[\left( { - \infty ,{1 \over 3}} \right)\]
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