Derivative Flashcards
What is a derivative?
slope of a tangent line
what does a positive derivative mean?
f(x) has a positive rate of change, therefore increasing
what does a negative derivative mean?
f(x) has a negative rate of change, therefore decreasing
what is f(x) at x0?
the instantaneous rate of change
what is the fundamental theorem on existence
each trajectory has it’s own set path
how do we represent when r is inversely proportional to c?
r/c
what is the reason for sketching vector fields?
to compute a specified number of change vectors
what does the numeration in the carrying capacity fraction mean
the population of the species
what does the denominator in the carrying capacity fraction mean
the limited amount of resources
explain what f(x1)-f(x0)/x1-x0 means
f(x1)-f(x0) represents the rate of change over the interval of
determinism
when you choose a certain vector in the vector field, the path of a trajectory is already pre-determined and there is only one way forward and one way backward
why can’t trajectories touch
there can only be one vector for each point in the vector field, therefore the trajectories cannot cross going into different directions
when do you square a variable in a differential equation?
when something is proportional to the same variable and make sure that it is mentioned that they are
logistic growth
when a growth is limited, such as carrying capacity
A′= 0.1A −0.01A^2 −0.5AB
what is 0.1A-0.01A^2 equal to?
0.1A(1-A/10)
