Question

英语翻译Prove that the curves y=x^3 and y=(x+1)/(x^2 +4) have ex

Answer 1

y = x³ = (x + 1)(x² + 4) = x³ + x² + 4x + 4

x² + 4x + 4 = (x + 2)² = 0

x = -2

The common point is (-2, -8)

y = x³, y' = 2x²; x = -2, y' =2*(-2)² = 8

y = (x + 1)(x² + 4)

y' = x² + 4 + (x + 1)*2x = 3x² + 2x + 4

x = -2, y' = 3(-2)² +2(-2) + 4 = 12