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) = 1x³ − 1x² + 3x + 4.
Working
- 1Differentiate term by term: f′(x) = 3x² − 2x + 3.
- 2Plug in x = 2: f′(2) = 3·(2)² − 2·(2) + 3.
- 3f′(2) = 12 − 4 + 3 = 11.