Calculus POD #18 Use the Definition of the Derivative to find d/dx(ax^2 + bx + c)

We're going to use the limit definition of a derivative to find the derivative of a quadratic function.

Bonus math: Notice that we get 2ax + b as our answer. If we want to know where the vertex of the parabola is, that would be where the derivative (slope) equals zero. So

2ax + b = 0
Solving for x gives us
x = -b/2a

That's the formula that we all learn in algebra for finding the vertex of a parabola! :)