AP Calculus - Review 5.1-5.5

If a function has a derivative that is negative, what does that tell you?

• The function is increasing
• The function is decreasing
• The concavity of the function is up
• The concavity of the function is down

Find the point(s) of inflection (if it exists) of the graphed function. 

• No point of inflection 

• Points b and g

• Points  b, f and g

• Points  a, b, c, d, e, f, g, and h

• Points a, c, e, f and h

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

• 0

• 1

• 2

• 3

Tags

CCSS.HSF.IF.B.6

• IVT

• EVT

• MVT

Which of these is NOT a hypothesis of the Mean Value Theorem (MVT)?

• A closed interval

• A differentiable function

• A continuous function

• A twice-differentiable function

Tags

CCSS.HSF.IF.B.6

What does the Extreme Value Theorem remind us to do?

• Check the endpoints! They might be the max/min.

• Check the inflection points! They might be the max/min.

• Check the endpoints! They give the secant slope.

• Check the inflection points! They are when the derivative is 0.

Tags

CCSS.HSF.IF.C.7

• Increasing and concave upward

• decreasing and concave upward

• increasing concave downward

• decreasing concave downward

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

• Relative maximum

• Relative minimum

• point of inflection

• cannot be determined

Tags

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.4

• A relative maximum at x=a

• A relative minimum at x=a

• No relative extrema at x=a

• A vertical tangent line at x=a

• a relative maximum at x=a

• a relative minimum at x=a

• no relative extrema at x=a

• a vertical tangent line at x=a

Tags

CCSS.HSF.IF.C.7