BitWithBite
Mathematics Worksheet
🧗 Gradient
SCORE___ / 20
NameClassDate
After this worksheet you can
Compute the gradient ∇f = (fx, fy).Evaluate the gradient at a point.Interpret the gradient as the direction of steepest increase.Find critical points where ∇f = 0.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1∇f for f(x,y) = 5x2 + 2y = ?
2∇f for f(x,y) = x3 + y2 at (2,1) = ?
3The gradient points in the direction of:
4Critical points satisfy:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5The gradient is ∇f = .
6∇f for f = 5x2 + 2y = .
7Find the gradient of f(x,y) = 5x2 + 2y.
8Find the gradient of f(x,y) = x3 + y2 at (2,1).
9Find the gradient of f(x,y) = x2y at (1,4).
🚀 Section C · Challenge ● CHALLENGE 5
10Find where ∇f = (0,0) for f(x,y) = x2 + y2 − 4x.
💭 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-A 2-A 3-B 4-A | 5 (fx, fy) 6 (10x, 2) 7 = (10x, 2) 8 = (12, 2) 9 = (8, 1) | 10 = x = 2, y = 0