Applications of Derivatives

Locate the absolute extrema of the function on the given interval.  

• Minimum at (1, -1/2), Maximum at (0,0)
• Minimum at (-1, -5/2), Maximum at (2,2)
• Minimum at (1, 5/2), Maximum at (2,2)
• Minimum at (1, 1/2), Maximum at (2,2)

Tags

CCSS.HSA.APR.B.3

Locate the absolute extrema of the function on the given interval.  

• Minimum at (π, -3), Maximums at (0,3) and (2π, 3)
• Minimum at (π, -3), Maximum at (0,3)
• Minimum at (π, -3), Maximum at (2π, 3)
• Minimum at (π, 3), Maximums at (0,3) and (2π, 3)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.TF.B.5

Determine whether Rolle's Theorem can be applied.  

• Yes
• No

Determine whether the Mean Value Theorem can be applied. 

• Yes
• No

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

CCSS.HSF.IF.B.5

Determine where the function is increasing and decreasing.  

• Decreasing on (-∞, -2) and Increasing on (-2, ∞)
• Decreasing on (-∞, 2) and Increasing on (2, ∞)
• Increasing on (-∞, -2) and Decreasing on (-2, ∞)
• Decreasing on (-∞, 4) and Increasing on (4, ∞)

Tags

CCSS.HSA.REI.D.10

Find the relative maximum and relative minimum of the function.  

• Relative Maximum at x=2, and Relative Minimum at x=-1
• Relative Maximum at x=2, and Relative Minimum at x=1
• Relative Maximum at x=-2, and Relative Minimum at x=1
• Relative Maximum at x=4, and Relative Minimum at x=1

Tags

CCSS.HSA.REI.D.10

CCSS.HSA.APR.B.3

Find the points of inflection on the given function.  

• (-2, -8)
• (0, 0)
• (-2, -8) and (0, 0)
• (2, 8) and (0, 0)

Tags

CCSS.HSA.REI.D.10

Determine where the function is concave up and concave down.  

• Concave Down on (-∞, 2), Concave Up on (2, ∞)
• Concave Up on (-∞, 2), Concave Down on (2, ∞)
• Concave Down on (-∞, -2), Concave Up on (-2, ∞)
• Concave Up on (-∞, -2), Concave Down on (-2, ∞)

Tags

CCSS.HSA.REI.D.10

Find the limit.  

• 2
• 1
• 0
• ∞

Tags

CCSS.HSA.APR.A.1

CCSS.HSA.APR.D.6

CCSS.HSA.APR.D.7

Find the limit.  

• 0
• -∞
• ∞
• -1