Taking the Derivative and Derivative Practice
The equation defining the derivative is given at left, as well as some notation to describe it.
If we have a polynomial function f, and f=Ctᵑ, then we can get the slope at every time t by defining a new function df/dt. This notation is meant to remind you of the slope formula: we use df/dt instead of Δf/Δt when the slope is that of a tangent line: when t2 and t1 are so close together that Δt approaches zero.
I've applied the equation twice to go from the brown position function to the pink acceleration function. Some of the notation used on the second brown line came from a good idea a 5th period student had in APCM at Manchester HS in the 2018-19 School year
Taking the Derivative and Derivative Practice
The equation defining the derivative is given at left, as well as some notation to describe it.
If we have a polynomial function f, and f=Ctᵑ, then we can get the slope at every time t by defining a new function df/dt. This notation is meant to remind you of the slope formula: we use df/dt instead of Δf/Δt when the slope is that of a tangent line: when t2 and t1 are so close together that Δt approaches zero.
I've applied the equation twice to go from the brown position function to the pink acceleration function. Some of the notation used on the second brown line came from a good idea a 5th period student had in APCM at Manchester HS in the 2018-19 School year