AP Calc Warmup April 27th

TRUE OR FALSE?  If f is continuous on [-1,1], f(-1)=4 and f(1)= -2, then there is a zero between -1 and 1.

• TRUE
• FALSE
• CANNOT BE DETERMINED

Which value is guaranteed by the MVT for the function given: f(x) = x² - 6x + 8 on [0,3]

• f(c) = 10

• f(c) = 4

• f ' (c) = -3

• f ' (c) = 7/3

Let g be a continuous function of the closed interval [-1, 3]. If g(-1)=-10 and g(3) = 6, which of the following are guaranteed? 

• g(0) = 0
• g'(c)= 0 for some c in (-1,3)
• g'(c)= 4 for some c in (-1, 3)
• g(c)= 4 for some c in (-1, 3)

Let g be a function that is differentiable over the interval (2, 9) . Giveng(3) = 5 , g(6) = -2 , and g(8) = 5 , which of the following must be true?
I. g has at least one horizontal tangent line.
II. g has at least 2 zeros.
III. For some c in the interval (3, 6), f'(c) = -7/3. 

• II only
• II and III
• I and II
• I, II, and III

h(x) is a differentiable function that contains the points (2, -5) and (5, 4). Which of the following must be true?

• h(x) is increasing over the interval (2, 5) 
• h(x) intercepts the x – axis at 113
• h'(c) =0 for some c in the interval (-5, 4).
• h'(c) = 3 for some c in (2, 5)

• 2/3 x³
• 2x+C
• 4x+C
•  2/3 x³ +C 

Another word for 'integral' is .. .

• Constant

• Derivative

• Antiderivative

• Theorem

Find the area under a curve defined by the equation 5x⁴+3x+7 between the x values 0 and 4.

• 1200
• 1/12
• 1134
• 1076

• The time it took for the town to grow from a population of 2 people to a population of 4 people.

• The number of people in the town on the fourth year.

• The average rate at which the population grew between the second and the fourth year.

• The change in the number of people between the second and the fourth year.

Which one of the definite integrals below gives the volume of the solid?