Labware - MA35 Multivariable Calculus - Single Variable Calculus





The derivative f '(x) of a function f(x) for some value of x, x0, is the instantaneous slope of the graph of the function at the point (x0, f(x0)).

We can find the derivative of f(x) at x = x0 using the limit definition of a derivative:

For a difference Δx in x, f '(x) equals the limit as Δx approaches 0 of

[f(x + Δx) - f(x)]/Δx



  • 1. Type in any linear function for f(x) and then try changing the size of Δx. Why is the accuracy of the approximation independent of Δx here?
  • 2. Use |x| (type "abs(x)") for f(x), and set x0 equal to 0. Try a small, positive value for Δx and then try a small negative value. What problem arises?