AP Calculus AB Final Multiple Choice
Exam Questions with Complete
Solutions
Find all points of relative minima and maxima:
y = x^2 + 6x + 5 - ANSWER-minima at (-3, -4)
Find all points of relative minima and maxima:
y = -12/(x^2 + 3) - ANSWER-minima at (0, -4)
Find the open intervals where the function is concave up and concave down.
y = (2x-12)^(1/3) - ANSWER-concave up: (-∞, 6)
concave down: (6, ∞)
Find the open intervals where the function is concave up and concave down.
y = -x^3 + x^2 + 3 - ANSWER-concave up: (-∞, 1/3)
concave down: (1/3, ∞)
Find x-coordinates of all points of inflection.
y = -4/(x^2 + 4) - ANSWER-POIs: x = -2/√(3), 2/√(3)
Find open intervals where function is increasing and decreasing.
f(x) = (6x^2 - 6)/x^3 - ANSWER-inc: (-√(3), 0)∪(0, √(3))
dec: (-∞, -√(3))∪(√(3), ∞)
Find open intervals where function is increasing and decreasing.
f(x) = -[(x+2)/(x+3)]^3 - ANSWER-inc: (-3, -2)
dec: (-∞, -3)∪(-2, ∞)
Find the x-coordinates of all critical points.
f(x) = -x^3 + x^2 + 4 - ANSWER-x = 0, 2/3
A particle moves along a horizontal line. Its position function is s(t) for t >= 0. Find the
velocity function v(t).
, s(t) = t^3 - 14t^2 - ANSWER-v(t) = 3t^2 - 28t
A particle moves along a horizontal line. Its position function is s(t) for t >= 0. Find the
acceleration function a(t).
s(t) = -t^3 + 9t^2 - ANSWER-a(t) = -6t + 18
Find equation of the line tangent to the function at the given point.
y = -ln(x + 1) at (2, -ln3) - ANSWER-y = -(1/3)x + 2/3 - ln3
Find equation of the line tangent to the function at the given point.
y = -3/(x^2 + 1) at (3, -3/10) - ANSWER-y = (9/50)x - 42/50
Find the indicated derivative with respect to x.
y = 5x^(5/4) + 2x^(1/3) + 4x^(1/5); Find (d^2*y)/(d*x^2) - ANSWER-(d^2*y)/(d*x^2) =
25/(16x^(3/4)) - 4/(9x^(5/3)) - 16/(25*x^(9/5))
Find the indicated derivative with respect to x.
y = 2/x^2; Find (d^2*y)/(d*x^2) - ANSWER-(d^2*y)/(d*x^2) = 12/x^4
Differentiate with respect to x.
y = 4x^(x^2) - ANSWER-dy/dx = 4x^(x^2)(2xlnx + x)
Differentiate with respect to x.
y = ln(2 + e^(3x^3)) - ANSWER-dy/dx = (e^(3x^3)*9x^2)/(e^(3x^3) + 2)
Find intervals on which the function is continuous.
f(x) = (x-2)/(x^2 + x - 6) - ANSWER-(-∞, -3)∪(-3, ∞)
Evaluate the limit.
limx->-3^- (-(x+3)/(x^2 + 5x + 6)) - ANSWER-1
limh->0 (√(2+h) - √2)/h - ANSWER-√2/4
Asked to create a movie poster with a 162 in^2 photo surrounded by a 4 in border at the
top and bottom and a 2 in border on each side. What overall dimensions for the poster
should the designer choose to use to least amount of paper? - ANSWER-13 in by 26 in.
Exam Questions with Complete
Solutions
Find all points of relative minima and maxima:
y = x^2 + 6x + 5 - ANSWER-minima at (-3, -4)
Find all points of relative minima and maxima:
y = -12/(x^2 + 3) - ANSWER-minima at (0, -4)
Find the open intervals where the function is concave up and concave down.
y = (2x-12)^(1/3) - ANSWER-concave up: (-∞, 6)
concave down: (6, ∞)
Find the open intervals where the function is concave up and concave down.
y = -x^3 + x^2 + 3 - ANSWER-concave up: (-∞, 1/3)
concave down: (1/3, ∞)
Find x-coordinates of all points of inflection.
y = -4/(x^2 + 4) - ANSWER-POIs: x = -2/√(3), 2/√(3)
Find open intervals where function is increasing and decreasing.
f(x) = (6x^2 - 6)/x^3 - ANSWER-inc: (-√(3), 0)∪(0, √(3))
dec: (-∞, -√(3))∪(√(3), ∞)
Find open intervals where function is increasing and decreasing.
f(x) = -[(x+2)/(x+3)]^3 - ANSWER-inc: (-3, -2)
dec: (-∞, -3)∪(-2, ∞)
Find the x-coordinates of all critical points.
f(x) = -x^3 + x^2 + 4 - ANSWER-x = 0, 2/3
A particle moves along a horizontal line. Its position function is s(t) for t >= 0. Find the
velocity function v(t).
, s(t) = t^3 - 14t^2 - ANSWER-v(t) = 3t^2 - 28t
A particle moves along a horizontal line. Its position function is s(t) for t >= 0. Find the
acceleration function a(t).
s(t) = -t^3 + 9t^2 - ANSWER-a(t) = -6t + 18
Find equation of the line tangent to the function at the given point.
y = -ln(x + 1) at (2, -ln3) - ANSWER-y = -(1/3)x + 2/3 - ln3
Find equation of the line tangent to the function at the given point.
y = -3/(x^2 + 1) at (3, -3/10) - ANSWER-y = (9/50)x - 42/50
Find the indicated derivative with respect to x.
y = 5x^(5/4) + 2x^(1/3) + 4x^(1/5); Find (d^2*y)/(d*x^2) - ANSWER-(d^2*y)/(d*x^2) =
25/(16x^(3/4)) - 4/(9x^(5/3)) - 16/(25*x^(9/5))
Find the indicated derivative with respect to x.
y = 2/x^2; Find (d^2*y)/(d*x^2) - ANSWER-(d^2*y)/(d*x^2) = 12/x^4
Differentiate with respect to x.
y = 4x^(x^2) - ANSWER-dy/dx = 4x^(x^2)(2xlnx + x)
Differentiate with respect to x.
y = ln(2 + e^(3x^3)) - ANSWER-dy/dx = (e^(3x^3)*9x^2)/(e^(3x^3) + 2)
Find intervals on which the function is continuous.
f(x) = (x-2)/(x^2 + x - 6) - ANSWER-(-∞, -3)∪(-3, ∞)
Evaluate the limit.
limx->-3^- (-(x+3)/(x^2 + 5x + 6)) - ANSWER-1
limh->0 (√(2+h) - √2)/h - ANSWER-√2/4
Asked to create a movie poster with a 162 in^2 photo surrounded by a 4 in border at the
top and bottom and a 2 in border on each side. What overall dimensions for the poster
should the designer choose to use to least amount of paper? - ANSWER-13 in by 26 in.
