AP Calculus AB Derivative Applications Test Prep

• -2

• 1/4

• -1/2

• 1/2

• 2

The graph shows the velocity v(t) in meters per second of a body moving along the coordinate line. When does the body change direction?

• t=2 and t=7

• t=1, 3, 6, and 8

• t=1 and t=8

• t=0, 2, 7, and 10

Tags

CCSS.HSF.IF.B.4

Rachael is blowing up a balloon so that the diameter increases at the rate of 10 centimeters per second. At what rate must she blow air into the balloon when the diameter measures 4 cm? (V=4/3 π r³)

• 6π cm³/second

• 8π cm³/second

• 60π cm³/second

• 6 cm³/second

The total number of all extrema of the function F whose derivative is F^'(x)=x(x-3)²(x-1)⁴ is

• 0

• 1

• 2

• 3

• None of these

Assume Clark and Lana leave Smallville Stadium from the same point at the same time. If Clark runs south at 4 mph and Lana runs west at 3 mph, how fast will the distance between Clark and Lana be changing at 10 hours?

• 5 mph

• 20 mph

• 25 mph

• 250 mph

Find the sum of the values a and b such that F(x)=2ax²+bx+3 has a relative extremum at (1, 2)

• 3/2

• -3/2

• 1

• -1

• None of these

The function M(x)=x⁴-4x² has

• one relative minimum and two relative maxima

• one relative minimum and one relative maximum

• no relative minima and two relative maxima

• two relative minima and no relative maxima

• two relative minima and one relative maximum

If y=ln(x²+y²) then the value of y' at (1,0) is

• 0

• -1

• 1

• 2

• undefined

A particle P moves along the coordinate line so that the graph is its position x(t) for time t in the interval [0,6]. When is P moving to the left?

• (2,3)U(5,6)

• (0,1)

• (1,2)U(3,5)

• (2.5,6)

Tags

CCSS.8.EE.B.5

The intervals for which the function F(x)=x⁴-4x³+4x²+6 increases are

• x<0, 1<x<2

• only x>2

• 0<x<1, x>2

• only 0<x<1

• only 1<x<2