Four Numbers in a Column, and Two Are Endpoints

You'll learnto find the highest and lowest values on a closed interval: list the critical points inside, add both ends, and compare values of f.

On a closed interval a continuous function really does reach a highest and a lowest value. Finding them is a short list and one column of numbers, and almost nobody gets the arithmetic wrong. What goes wrong is the list, or the column. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · EVERY CRITICAL POINT INSIDE, PLUS BOTH ENDS · v2

f(x) = x³ − 3x² − 9x + 5 ON [−2, 6] ⇒ CANDIDATES −2, −1, 3, 6

Before you start

What you're looking at

One cubic, f(x) = x³ − 3x² − 9x + 5, drawn only across the closed interval [−2, 6]. A dashed wall stands at each end.

The question

Which input on this interval gives the largest value of f, and which gives the smallest?

Step 1 / 12