The derivative of a functionf is a new function f. The domain of f us a subset of the domain of f. The derivative has various applications and interpretations, including:

For each x in the domain of f, f(x)is the [ Select ] ["asymptote", "secant", "slope", "intercept"] of the line tangent to the graph of f at the point (x,f(x)).

For each x in the domain of f, f(x)is the [ Select ] ["slope", "instantaneous", "average", "velocity"] rate of change of y=f(x) with respect to x.

If f(x) is the position of a moving object at time x, then v=f(x) is the [ Select ] ["speed", "acceleration", "velocity", "mass"] of the object at that time.