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) = 4x³ + 2x² + 6x + 5.
Working
- 1Differentiate term by term: f′(x) = 12x² + 4x + 6.
- 2Plug in x = -2: f′(-2) = 12·(-2)² + 4·(-2) + 6.
- 3f′(-2) = 48 − 8 + 6 = 46.