When a Piecewise Max Exists

Problem

Let

f(x) = \begin{cases} ax - 2, & x < a,\\ 3x - x^2, & x \geqslant a. \end{cases}

1. Give one value of $a$ for which $f(x)$ has no maximum value. 2. Find the range of values of $a$ for which $f(x)$ has a maximum value.

Answer

Solution

Difficulty	6/10
Topics	functions, Extrema, Casework

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