Quiz

Question 1 · easy

Find the rectangle of maximum area with perimeter 40.

Question 2 · medium

Minimize f(x) = x^2 + 16/x for x > 0.

Question 3 · medium

Find the minimum sum of two positive numbers whose product is 25.

Question 4 · medium

A box with square base and open top holds 500 cm^3. Find the base side that minimizes surface area.

Question 5 · easy

A company has P = -2x^2 + 80x - 400. How many units maximize profit?

Question 6 · easy

Find the maximum profit from Question 5.

Question 7 · medium

Find the absolute max of f(x) = x^2 - 4x + 3 on [0, 4].

Question 8 · challenge

Two numbers sum to 20. Maximize the product of their squares.

Question 9 · challenge

A rectangle has one side on the x-axis with corners at (x,0), (-x,0), (-x,y), (x,y) on the curve y=9-x^2. Find the maximum area.

Question 10 · challenge

Find the minimum distance from the origin to the line y = 2x + 5.