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Differentiation Quiz - MCQ Questions with Solutions
Question 1
If f(x) = (x2 + 1)/(x + 1), what is f'(x)?
- A
(x2 + 2x + 1)/(x + 1)2
- B
(2x + 1)/(x + 1)
- C
(2x - 1)/(x + 1)2
- D
(2x - 1)/(x + 1)
Question 2
If f(x) = sqrt(x)sin(x), what is f''(x), the second derivative?
- A
sqrt(x)cos(x) - 2sin(x)/√(x)
- B
sqrt(x)cos(x) + 2sin(x)/√(x)
- C
sqrt(x)cos(x) - sin(x)/√(x)
- D
sqrt(x)cos(x) + sin(x)/√(x)
Question 3
If g(x) = ln(2e^(-x) + 3), what is g'(x)?
- A
-e^(-x)/(2e^(-x) + 3)
- B
e^(-x)/(3 - e^(-x))
- C
-e^(-x)/(3 - e^(-x))
- D
-e^(-x)/(2e^(-x) + 3)
Question 4
If h(x) = sin^2(x)e^x, what is h''(x), the second derivative?
- A
2e^(sin^2(x))cos(x)sin(x)
- B
e^(sin^2(x))cos(x)sin(x)
- C
2e^(sin^2(x))cos^2(x)
- D
e^(sin^2(x))cos^2(x)
Question 5
If f(x) = x^3 + 2x^2 - 4x + 1, what is the absolute minimum value of f(x)?
- A
-∞
- B
-8
- C
1
- D
2
Question 6
If f(x) = x^3 - 4x^2 + 5x + 2, what is the interval where f(x) is concave upward?
- A
(-∞, 2)
- B
(2, ∞)
- C
(1, ∞)
- D
(-∞, 1)
Question 7
If h(x) = x^3e^(-2x^2), what is h''(x), the second derivative?
- A
-4x^3e^(-2x^2) - 12xe^(-2x^2)
- B
-6x^2e^(-2x^2) + 4x^4e^(-2x^2)
- C
6x^2e^(-2x^2) - 4x^4e^(-2x^2)
- D
Apply the product rule twice.4x^3e^(-2x^2) + 12xe^(-2x^2)
Question 8
If h(x) = ln(1 + e^(-2x)), what is h'(x)?
- A
2e^(-2x)/(1 + e^(-2x))
- B
-2e^(-2x)/(1 - e^(-2x))
- C
-2e^(-2x)/(1 - e^(-2x))
- D
2e^(-2x)/(1 + e^(-2x))
Question 9
If h(x) = 2x^3 - 5x^2 + 3, what is the point(s) of inflection?
- A
x = 1
- B
x = 2
- C
x = 3
- D
None of the above
Question 10
What is the derivative of ln(1 + e^(-x))?
- A
-e^(-x)/(1 + e^(-x))
- B
e^(-x)/(1 - e^(-x))
- C
-e^(-x)/(1 - e^(-x))
- D
-e^(-x)/(1 + e^(-x))
There are 25 questions to complete.
