h(x)=-2x^3 on [x, x+h]

Question

Find the rate of change for the expression:

h(x)=-2x^3 with the interval [x, x+h]

Answer 1

f(x) = -2x³

[f(x+h) - f(x)] / (x+h-x)

= [-2(x+h)³ + 2x³] / h

= [-2(x³ + 3x²h + 3xh² + h³) + 2x³] / h

= [-6x²h - 6xh² - 2h³] / h

= h(-6x² - 6xh - 2h²) / h = -6x² - 6xh - 2h²