Second Derivatives Flashcards

All 4 cards in this deck

What does $\frac{d^2y}{dx^2}$ mean?

The derivative of $\frac{dy}{dx}$ — differentiate the function twice.

What does the second derivative measure?

The rate of change of the gradient function.

What notation is used for the second derivative of $f(x)$?

$f''(x)$.

What are the steps to find $\frac{d^2y}{dx^2}$?
e.g. $y = x^3 - 3x^2$

1. Differentiate once: $\frac{dy}{dx} = 3x^2 - 6x$
2. Differentiate the result again: $\frac{d^2y}{dx^2} = 6x - 6$