R''(t) = rac{d}{dt}(9t^2 - 10t + 2) = 18t - 10.

Mon, 04 May 2026 13:08:45 +0000

Understanding the Derivative: R''(t) = d²/dt²(9t² - 10t + 2) and the Beauty of Calculus When studying calculus, one of the most fundamental concepts is differentiation—the process of determining how functions change with respect to their input variables. For students and math enthusiasts alike, understanding the second derivative, especially in the context of polynomial functions, deepens insight into motion, optimization, and curve behavior. ### What Is R''(t)? The notation R''(t) represents the second derivative of a function R(t) with respect to t. It measures the rate of change of the first derivative, R'(t), and provides critical information about the function’s concavity, acceleration, and inflection points. For a quadratic function like $$ R(t) = 9t^2 - 10t + 2, $$ the first derivative is: $$ R'(t) = rac{d}{dt}(9t^2 - 10t + 2) = 18t - 10. $$ This first derivative describes the instantaneous rate of change of R(t)—essentially, the slope of the tangent line at any point on the parabola.