The Least $m$

★ 6/10Extrema calculus Monotonicity inequality

Problem

Let $f(x) = x\ln x - 3x$ .

1. Find the extreme values of $f(x)$ . 2. If the inequality

f(x) \geqslant mx^2 - 3x + \frac{2}{m}

holds for all $x$ in the domain, find the minimum value of the real number $m$ .

Answer

Solution

Difficulty	6/10
Topics	Extrema, calculus, Monotonicity, inequality

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