Module 9 - The Relationship between a Function and Its First and Second Derivative
 
  Introduction | Lesson 1 | Lesson 2 | Self-Test
 
 Self Test
 

    Define f(x) = –x3 + 2x2 + 4x –3 and graph it in a [-7.9, 7.9] x [-6, 6] window.

  1. Use the Derivative feature of the Graph Math menu to find f '(1.5).
  2. Use the Tangent feature of the Graph Math menu to find the equation of the tangent line to
    y = f(x) at x = 1.5.
  3. Refresh the graph screen by pressing and use the Inflection feature of the Graph Math menu to find the inflection point of y = f(x).
  4. Find the intervals where the graph of f is concave upward and where it is concave downward.
  5. Display the graphs of the function f and its derivative and use the graph of the derivative to determine where the turning points of f occur.
  6. Use the graph of the derivative of f to determine where f is increasing and where f is decreasing.
  7. Use the Derivative key to find the second derivative of

Click here to check your answers.


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