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 + 3x² − 4x + 2.
Working
- 1Differentiate term by term: f′(x) = 3x² + 6x − 4.
- 2Plug in x = -2: f′(-2) = 3·(-2)² + 6·(-2) − 4.
- 3f′(-2) = 12 − 12 − 4 = -4.