AP Calculus Exam Practice - Derivatives Focus I

• Undefined

• continuous but not differentiable

• differentiable but not continuous

• neither continuous nor differentiable

• both continuous and differentiable

Tags

CCSS.HSF-IF.C.7B

• -1

• 0

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

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• 
• 
• 

The function f is differentiable and has values as shown in the table here. Of the following, on which interval is the average rate of change of f greatest?

• [0,2]

• [2,6]

• [6,12]

• [12,20]

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

• 1

• 0

• -1

• DNE

• (0,0) only

• (1/2,1/5) only

• (0,0) and (-4,2)

• (0,0) and (4,2/3)

• there are no such points

In the xy-plane, the line x + y = k , where k is a constant, is tangent to the graph of y = x² + 3x + 1 . What is the value of k ?

• -3

• -2

• -1

• 0

• 1

At time t=0, a storage tank is empty and begins filling with water. For t>0 hours, the depth of the water in the tank is increasing at a rate of W(t) feet per hour. Which of the following is the best interpretation of the statement W′(2)>3?

• Two hours after the tank begins filling with water, the depth of the water is increasing at a rate greater than 3 feet per hour.

• Over the first two hours after the tank begins filling with water, the depth of the water is always increasing at a rate greater than 3 feet per hour.

• Two hours after the tank begins filling with water, the rate at which the depth of the water is rising is increasing at a rate greater than 3 feet per hour per hour.

• Over the first two hours after the tank begins filling with water, the rate at which the depth of the water is rising is always increasing at a rate greater than 3 feet per hour per hour.

Tags

CCSS.HSF.IF.B.4

The figure here shows the graph of a function f, which has a vertical tangent at x=2 and a horizontal tangent at x=4. Which of the following statements is false?

• f is not differentiable at x=-1 because the graph of f has a jump discontinuity at x=-1.

• 
  f is not differentiable at x=2 because the graph of f has a vertical tangent at x=2.

• f is not differentiable at x=4 because the graph of f has a horizontal tangent at x=4.

• f is not differentiable at x=6 because the graph of f has a removable discontinuity at x=6.