 |
VOOZH | about |
|
VOOZH | about |
Question 1
If f(x) = (x^2 + 1)/(x + 1), what is f'(x)?
(2x + 1)/(x + 1)^2
(2x + 1)/(x + 1)
(2x - 1)/(x + 1)^2
(2x - 1)/(x + 1)
Question 2
If f(x) = sqrt(x)sin(x), what is f''(x), the second derivative?
sqrt(x)cos(x) - 2sin(x)/√(x)
sqrt(x)cos(x) + 2sin(x)/√(x)
sqrt(x)cos(x) - sin(x)/√(x)
sqrt(x)cos(x) + sin(x)/√(x)
Question 3
If g(x) = ln(2e^(-x) + 3), what is g'(x)?
-e^(-x)/(2e^(-x) + 3)
e^(-x)/(3 - e^(-x))
-e^(-x)/(3 - e^(-x))
-e^(-x)/(2e^(-x) + 3)
Question 4
If h(x) = sin^2(x)e^x, what is h''(x), the second derivative?
2e^(sin^2(x))cos(x)sin(x)
e^(sin^2(x))cos(x)sin(x)
2e^(sin^2(x))cos^2(x)
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)?
-∞
-8
1
2
Question 6
If f(x) = x^3 - 4x^2 + 5x + 2, what is the interval where f(x) is concave upward?
(-∞, 2)
(2, ∞)
(1, ∞)
(-∞, 1)
Question 7
If h(x) = x^3e^(-2x^2), what is h''(x), the second derivative?
-4x^3e^(-2x^2) - 12xe^(-2x^2)
-6x^2e^(-2x^2) + 4x^4e^(-2x^2)
6x^2e^(-2x^2) - 4x^4e^(-2x^2)
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)?
2e^(-2x)/(1 + e^(-2x))
-2e^(-2x)/(1 - e^(-2x))
-2e^(-2x)/(1 - e^(-2x))
2e^(-2x)/(1 + e^(-2x))
Question 9
If h(x) = 2x^3 - 5x^2 + 3, what is the point(s) of inflection?
x = 1
x = 2
x = 3
None of the above
Question 10
What is the derivative of ln(1 + e^(-x))?
-e^(-x)/(1 + e^(-x))
e^(-x)/(1 - e^(-x))
-e^(-x)/(1 - e^(-x))
-e^(-x)/(1 + e^(-x))
There are 25 questions to complete.
