L'Hopital's and Concavity Quick Quiz

• pi

• -1

• 1

• -pi

Tags

CCSS.HSF.TF.A.1

CCSS.HSF.TF.A.2

CCSS.HSF.TF.A.3

CCSS.HSF.TF.C.8

CCSS.HSG.C.B.5

Find

• 0

• DNE

• 3

• 1/3

Over what interval(s) is f(x) concave up? (Be careful this is a graph of f'!)

• (-1.5, ∞)

• (-3, 1)

• (-∞,-3) U (1, ∞)

• (-5, 0)U(2, ∞)

Let f be a polynomial function with values of f '(x) at selected values of x given in the table. Which of the following must be true for -2 < x < 6 ?

• The graph of f is concave up

• The graph of f has at least two points of inflection

• f is increasing

• f has no critical points

• f has at least two relative extrema

Let f be a function such that f(-1)=1. At each point (x, y) on the graph of f, the slope is given by f' = -x² - xy + y² - 1. Which statement is true?

• f has a relative minimum at x = -1

• f has a relative maximum at x = -1

• f has neither a relative minimum nor minimum at x = -1

• There is insufficient information to determine whether f has a relative maximum, minimum, or neither at x = -1