BitWithBite
Mathematics Worksheet
🏆 Optimization
SCORE___ / 20
NameClassDate
After this worksheet you can
Translate a word problem into an objective function.Use a constraint to reduce the problem to a single variable.Find maxima and minima by solving f′(x) = 0.Check endpoints for absolute extrema.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1A rectangle with perimeter 100 has maximum area with dimensions:
2Two numbers with sum 50 have maximum product when they are:
3To optimize, you first set ___ equal to 0:
4Minimize C(x) = 2x2 − 40x + 300; the minimum is at x =
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Set the first derivative equal to to find critical points.
6A rectangle of fixed perimeter has maximum area when it is a .
7A rectangle has perimeter 100. Find the dimensions that maximize area.
8Find two numbers with sum 50 whose product is maximum.
9Minimize C(x) = 2x2 − 40x + 300.
🚀 Section C · Challenge ● CHALLENGE 5
10Maximize P(x) = −x2 + 12x.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
Teacher's Signature
Parent's Signature
✂ answer key — fold or cut before handing out
1-B 2-A 3-B 4-B | 5 0 6 square 7 = 25 by 25 8 = 25 and 25 9 = Minimum at x = 10, C = 100 | 10 = Maximum at x = 6, P = 36