A Maximum With a Prescribed Value

★ 8/10functions Extrema Absolute Value Casework

Problem

Let $f(x) = x|x + a| + m|x - 1|$ .

1. For $a = 0$ , $m = 1$ , describe the monotonicity of $f$ . 2. If the maximum of $f$ on $[0, 2]$ equals $a + 1$ , find the range of $m$ (in terms of $a$ ).

Answer

Solution

Difficulty	8/10
Topics	functions, Extrema, Absolute Value, Casework

Whiteboard

Your sketch is saved only in this browser. To share it, export your drawing as an image (whiteboard menu → Export as → PNG), then upload that image in the comments below.

Discussion

Ask questions, share alternate solutions, and use LaTeX freely.

0 comments

No comments yet.