Updates Quiz 7 on Friday!
 Covers the entire new unit so far
 Extrema
 Rolle's Theorem
 Mean Value Theorem
 Increasing and Decreasing Functions
 First Derivative Test
Bell Ringer
 Rolle's Theorem and Mean Value Theorem
Determine whether Rolle’s Theorem can be applied to the function f(x) = x2  4x  5 on the closed interval [1, 5]. If Rolle’s Theorem can be applied, find all values of c in the open interval (1, 5) such that f’(c) = 0. Rolle’s Theorem applies; c = 2 Rolle’s Theorem applies; c = 0.5 Rolle’s Theorem does not apply. Rolle’s Theorem applies; c = 2 both a and d
Determine whether Mean Value Theorem can be applied to the function f(x) = x3 on the closed interval [0, 16]. If the Mean Value Theorem can be applied, find all numbers c in the open interval (0, 16) such that f’(c) = [f(b)  f(a)] / (b  a). MVT applies; c = 4 MVT applies; c = 16sqrt(3) / 3 MVT applies; c = 8 MVT applies; c = 16sqrt(3) / 3 MVT does not apply
Find the average value of f(x) = 2x3 + 3 on [3, 7] 689 158 158 4  none of the above
Review Prerequisites
 Interval Notation
 Maxima/Minima
 Zero Product Property
 Finding Minima/Maxima Graphically
 Extrema
Lesson Checkpoints (page 186)
 L  #6
 M  #20
 N  #44
 O  #48
Exit Ticket Posted on the board at the end of the class.
 Lesson Objective(s) How can the first derivative be used to find relative extrema?
 How can the first derivative be used to find intervals in which a function is increasing or decreasing?
Standard(s)  #1  Make sense of problems and persevere in solving them
 #2  Reason abstractly and quantitatively
 #5  Use appropriate tools strategically
 #6  Attend to precision
 #8  Look for and express regularity in repeated reasoning
Past Checkpoints  Extrema (page 169)
 A  #4
 B  #6
 C  #18
 D  #22
 E  #34
 Rolle's Theorem (page 176)
 Mean Value Theorem (page 176177)
