Local minimum and local maximum of a function (derivative method)
Find all turning points of a graph using derivatives

Find all turning points of a graph using derivatives

Suppose you want to find graphically all the turning points of the following function:

\[ f(x) = x^3 - 6x^2 + 11x - 6 \]

  1. Create a new document and select Add Graphs. Enter the function into f1(x).
  2. Enter f2(x) = \frac{df1(x)}{dx} by pressing Menu Icon and Enter Icon to graph the derivative of the function. Select only f2(x) to show only the derivative.
  3. Find the zeros of the derivative:
    1. Press Menu Icon and select Analyze Graph > Zero.
    2. Select lower and upper bounds between the crossing of the x-axis.
    3. Press Enter Icon. Repeat this process for the second zero.

    Recursive Formula Example

    The results should be \( x = 1.42 \) and \( x = 2.58 \) (rounded).