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AP Calculus AB Semester 1 Review - Applications of Derivatives Flashcards | StudBud
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AP Calculus AB Semester 1 Review - Applications of Derivatives
AP Calculus AB Semester 1 Review - Applications of Derivatives
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1
The radius of sphere increases at rate of 3 in/min. Find rate of change of volume when r=9 in.
dV/dt = 324π in3/min
dV/dt = 108π in3/min
dV/dt = 972π in3/min
2
Edges of a cube expand at rate of 6cm/s. How fast is volume changing when each edge is 2 cm?
dV/dt = 72 cm3/s
dV/dt = 144cm3/s
dV/dt = 36cm3/s
dV/dt = 24 cm3/s
3
Use Rolle's Theorem to find all c values on interval [0,3] for F(x)=-x
2
+3x, such that F'(c)=0
c = 3/2 and -3/2
c = 3/2
c = -3/2
4
Determine the concavity of the function F(x)=x
3
+6x
2
+12x
Concave Up on (-2,∞); Concave Down on (-∞,-2)
Concave Up on (2,∞); Concave Down on (-∞,2)
Concave Up on (-∞,2); Concave Down on (2,∞)
Concave Up on (-2,∞); Concave Down on (-∞,-2)
5
Locate the absolute extrema of the function F(x)=x
3
-12x on the interval [0,4].
Max at (-2,16); Min at (0,0)
Max at (4,16); Min at (2,-16)
Max at (4,16); Min at (0,0)
Max at (4,16) and (-2,16); Min at (2,-16)
6
Use Mean Value Theorem on interval [-2,1] for F(x)=x
2
to find c-values such that F'(c)=slope
c = 3/2
c = -3/2
c = -1/2
