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A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
$Interval \rightarrow Function$
Options:
$Interval \rightarrow Function$
Solution:
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Verified Answer
The correct answer is:
$\left(-\infty, \frac{1}{3}\right] \rightarrow \quad 3 x^2-2 x+1$
$\left(-\infty, \frac{1}{3}\right] \rightarrow \quad 3 x^2-2 x+1$
Clearly function $f(x)=3 x^2-2 x+1$ is increasing when $f^{\prime}(x)=6 x-2 \geq 0 \Rightarrow x \in[1 / 3, \infty)$
Hence $(C)$ is incorrect.
Hence $(C)$ is incorrect.
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