1) f(x) = 12(1 + ∛x)², f'(8) = ?
f(x) = 12(1 + ∛x)² = 12(1 + 2∛x + ∛x²) = 12 +24∛x + 12∛x² =
= 12 +12*x¹/³ + 12*х²/³
f'(x) = 12*1/3*х⁻²/³ + 12*2/3*х⁻¹/³ = 4/∛х² + 8/∛х
f'(8) = 4/∛8² + 8/∛8= 1 + 4 = 5
2)f(x) = 9 ∛x² + x , f'(27) = ?
f(x) = 9 ∛x² + x = 9*х²/³ + х
f'(x) = 9*2/3 * x⁻¹/³ + 1 = 6/∛х + 1
f'(27) = 6/∛27 +1 = 2 + 1 = 3