Extremes in Two Windows

★ 8/10Quadratic Equations Extrema calculus inequality

Problem

The function

f(x) = \frac{2}{3}x^3 + \frac{1}{2}ax^2 + 2bx + c

has a local maximum in $(0, 1)$ and a local minimum in $(1, 2)$ . If $(a + 3)b \leqslant t$ holds for all such $a, b$ , find the range of possible values of $t$ .

Answer

Solution

Difficulty	8/10
Topics	Quadratic Equations, Extrema, calculus, 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

No comments yet.