Derivative of a polynomial
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
f(x) = ax³ + bx² + cx + d → f′(x) = 3ax² + 2bx + c
Problem
Find f′(2) for f(x) = 3x³ − 3x² − 2x − 3.
Working
- 1Differentiate term by term: f′(x) = 9x² − 6x − 2.
- 2Plug in x = 2: f′(2) = 9·(2)² − 6·(2) − 2.
- 3f′(2) = 36 − 12 − 2 = 22.