3.16 Examples of rates of change

(i) The derivative is the gradient of the tangent to a graph; the derivative is the rate of change of $y$ with respect to $x$.

(ii) The interest rate is the rate of change of value of a dollar loan with respect to time.

(iii) Speed is the rate of change of position with respect to time; acceleration is the rate of change of speed with respect to time.

(iv) Power is the rate of change of energy with respect to time.