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Consider the function

\(\[ f(x) = \begin{cases} ax^2 & \text{if } x \geq a,\\ ax +2a& \text{if } x

where a is some number.

What is the largest value of a such that the graph of \(y=f(x)\) intersects every horizontal line at least once?

 Oct 25, 2020
 #1
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The largest possible value of a is 8.

 Oct 31, 2020

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