1,125 Answered Questions for the topic AP Calculus

Ap Calculus Math Calculus

01/01/20

Relation of Rates
The height of a cylinder with a fixed radius of 6 cm is increasing at the rate of 3 cm/min. Find the rate of change of the volume of the cylinder (with respect to time) when the height is... more
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Ap Calculus Math Calculus

01/01/20

Relation of Rates
The area A = πr2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 3ft?Options:  6π ft2/ft  3π ft2/ft  6 ft2/ft  9π ft2/ft more
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Ap Calculus Math Calculus

01/01/20

Relation of Rates
If y = x3 + 2x and  , find  when x = 2. Give only the numerical answer. For example, if  = 3, type only 3
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Ap Calculus Math Calculus

01/01/20

Applied Max and Min
If 600 cm2 of material is available to make a box with a square base and a closed top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without... more
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Ap Calculus Math Calculus

01/01/20

Applied Max and Min
What is the area of the largest rectangle with lower base on the x-axis and upper vertices on the curve y = 12 - x2?Options: 8 12 16 32
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Ap Calculus Math Calculus

01/01/20

Applied Max and Min
A farmer has 1,200 feet of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fence along the river. Write the function that will produce the largest area... more
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Ap Calculus Math Calculus

01/01/20

Applied Max and Min
Provide one of the two positive integers whose sum is 200 and whose product is a maximum.
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Ap Calculus Math Calculus

01/01/20

Applied Max and Min
Find the absolute maximum value of the function Options: 0 1 2 3
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Ap Calculus Calculus

01/01/20

Linearization and approximation
If f is continuous at x = c, then f is differentiable at x = c.Options: true false
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Ap Calculus Calculus

01/01/20

Linearization and approximation
The local linear approximation of a function f will always be greater than or equal to the function's value if, for all x in an interval containing the point of tangencyOptions: f '(x) < 0 f... more
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Ap Calculus Calculus

01/01/20

Linearization and approximation
If f(1) = 5 and  , which of the following is the best approximation for f(1.03) using local linearization? Options: 9.06 5.06 -4.94 -5.97
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Ap Calculus Calculus

01/01/20

Linearization and approximation
Which of the following is the best linear approximation for f(x) = sin(x) near x = π seconds?Options: y = -x + π - 1 y = -1 y = -x + π y = -x - π
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Ap Calculus Calculus

01/01/20

Distance, Velocity, Acceleration, and Rectilinear
A particle moves along the x-axis so that at any time t, measured in seconds, its position is given by s(t) = 5cos(t) - sin(3t), measured in feet. What is the acceleration of the particle at time t... more
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Ap Calculus Calculus

01/01/20

Distance, Velocity, Acceleration, and Rectilinear
The position of a particle on the x-axis at time t, t > 0, is s(t) = ln(t) with t measured in seconds and s(t) measured in feet. What is the average velocity of the particle for 1 ≤ t ≤... more
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Ap Calculus Calculus

01/01/20

Distance, Velocity, Acceleration, and Rectilinear
The driver of a car traveling at 60 ft/sec suddenly applies the brakes. The position of the car is s(t) = 60t - 3t2, t seconds after the driver applies the brakes. How many seconds after the driver... more
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Ap Calculus Calculus

01/01/20

Distance, velocity, acceleration, and rectilinear
A particle is moving along the x-axis so that its position at t ≥ 0 is given by s(t) = (t)In(5t). Find the acceleration of the particle when the velocity is first zero.Options: 5e 5e2 e None of... more
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Ap Calculus Calculus

01/01/20

Distance, Velocity, Acceleration, and Rectilinear
A particle moves with velocity function v(t) = 2t2 - 3t - 3, with v measured in feet per second and t measured in seconds. Find the acceleration of the particle at time t = 2 secondsOptions: 3/4... more
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Ap Calculus Calculus

01/01/20

Maximums and Minimums
The maximum value of f(x) = x3 - 3x2 - 9x + 2 on the interval [0, 6] isOptions: 2 56 135 There is no maximum on [0,6]
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Ap Calculus Calculus

01/01/20

Analyzing Functions
Find the critical point of the function f(x) = -x2 + 4x - 5.Options: (2 , -1) (2 , 0) (-2 , -37) (2 , 1)
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Ap Calculus Calculus

01/01/20

Analyzing Functions

Given the graph of f '(x), the derivative of f(x), which of the following statements are true about the graph of f(x)? I. The graph of f has a critical point at x = 0.II. The graph of f has a... more
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Ap Calculus Calculus

01/01/20

Analyzing Functions

Use the graph of f(x) below to estimate the value of f '(3):Options: -5 -1 0 1
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Ap Calculus Calculus

12/31/19

Implicit Differentiation
Find the slope of the graph of the relation x2y + 4y = 8 at the point (2, 1).Options: 1 3/2 1/2 -1/2
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Ap Calculus Calculus

12/31/19

Implicit Differentiation
Find  if f(x) = (x + 8)3xOptions: 3xln(x + 8) 3x(x + 8)(3x - 1)
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Ap Calculus Calculus

12/31/19

Implicit Differentition
If 2x2 + y2 = 17 then evaluate  when x = 2 and y = 3. Round your answer to 2 decimal places. Use the hyphen symbol, -, for negative values.
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Ap Calculus Calculus

12/18/19

Derivatives of Trig Functions
For f(x) = esin(x) use your graphing calculator to find the number of zeros for f '(x) on the closed interval [0, 2π].Options: 1 2 3 4
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