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Mathematics Worksheet
🧠Applications of Derivatives
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Use derivatives to find velocity and acceleration.Determine where a function is increasing or decreasing from the sign of f′.Find critical points by solving f′(x) = 0.Interpret the second derivative.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1If s(t) = t3 − 6t, the velocity at t = 2 is:
2A function f is increasing where:
3Critical points occur where:
4Acceleration is the derivative of:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Velocity is the derivative of .
6f is increasing where f′(x) 0.
7A particle's position is s(t) = t3 − 6t. Find the velocity at t = 2.
8Find the acceleration at t = 2 for that particle.
9For f(x) = x2 + 2x, find where f is increasing.
🚀 Section C · Challenge ● CHALLENGE 5
10For f(x) = −x2 + 4x, find where f is decreasing.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-B 2-A 3-B 4-B | 5 position 6 > (greater than) 7 = 6 8 = 12 9 = x > −1 | 10 = x > 2