Four Claims About a Cubic

★ 7/10functions Extrema calculus Monotonicity Vieta's Formulas

Problem

Let $f(x)=x(x-3)^2$ , and suppose $f(a)=f(b)=f(c)$ with $a<b<c$ . Determine, with proof, which of the following claims are true.

1. $1<a<2$ . 2. $a+b+c=6$ . 3. $a+b>2$ . 4. The range of $abc$ is $(0,4)$ .

Answer

Solution

Difficulty	7/10
Topics	functions, Extrema, calculus, Monotonicity, Vieta's Formulas

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.