Here we will be discussing the basics of a derivative of functions.
3.1 Derivative of a
– From 2.4 we defined slope of a curve of y = f(x) at
a point where x=a as
– When it exists, this limit is called the derivative
of f at a. f’(x) is the derivative of the function.
• Differentiable: a function is differentiable
at a point when the f’(x) exists
– If the function is differentiable at every point in
the domain, it is a differentiable function
Example 1: Differentiate
• Derivative at a point x=a:
Example 3: Use the alternative
derivative formula to differentiate at x = a
Example 4: Graph the derivative of
the given function.
Example 5: Sketch f given the
a.) f(0)=0 b.) The graph below is f’ c.) f is
• Right-Hand Derivative:
• Left-Hand Derivative:
Example 6: Show that there are LH
& RH derivatives at x = 0 but no derivative