p''(x) = 12x^2 - 24x + 12

Sun, 19 Apr 2026 04:11:16 +0000

# Understanding the Second Derivative: p''(x) = 12x² – 24x + 12 In calculus, derivatives play a fundamental role in analyzing functions—helping us determine rates of change, slopes, and curvature. One particularly insightful derivative is the second derivative, p''(x), which reveals the concavity of a function and aids in identifying points of inflection. In this article, we’ll explore the second derivative given by the quadratic expression: p''(x) = 12x² – 24x + 12 We’ll break down its meaning, how to interpret its graph, and why it matters in mathematics and real-world applications.