Extreme Value Theorem

If (a, b) is a relative minimum, then which of the following is true about f’(a)?

• It's zero.

• It's positive.

• It's negative.

• cannot be determined

1. What is the relative maximum of the graph shown?

• (2, 5)

• (0,1)

• (1, 0)

• (-1, 4)

Which of the following is the absolute maximum of the graph shown?

• (-1, 7)

• (2, -20)

• (-2.18, -8.81)

• (3.312, 0)

Which of the following extrema is the absolute minimum of the graph shown?

• (-1, 7)

• (2, -20)

• (-2.18, -8.81)

• (3.312, 0)

Which of the following extrema is the relative minimum of the graph shown?

• (-2, -47)

• (0, -3)

• (6, -111)

• (7, -101)

If (a, b) is a relative maximum, then which the following is TRUE about f’’(a)?

• It's positive.

• It's negative.

• It's zero.

• DNE

If (a, b) is a relative minimum, then which the following is TRUE about f’’(a)?

• It's zero.

• It's negative.

• It's positive.

• cannot be determined

Which of the following is the critical value of the function y = x² -4x -5?

• 0

• 2

• -2

• -9

 What are the critical values of   $y=\ x^3-x^2-8x+12?$  

•  $\left\{-\frac{4}{3},2\right\}$  

• {2, 3}

• {2, 4/3}

• (-4/3, 439/27)

What is the relative minimum point of the function y = x² - 6x + 4?

• (3, -5)

• (3,13)

• (-3,-5)

• (-5, 3)