18 Questions
What can be concluded about the function f5(x)?
It has a strict global maximum at x = 0.
What is the nature of the extreme values of the function f6(x)?
It has a strict local minimum at x = 2 and a strict global maximum at x = −3.
What is the nature of the function f7(x)?
It has no extreme values.
What can be concluded about the function f8(x)?
It has a strict local maximum at x = 1.
What can be said about the concavity of the function f1(x)?
It is weakly concave up and weakly concave down.
What can be said about the concavity of the function f3(x)?
It is strictly concave down on part of the real line and strictly concave up on the rest.
What is the nature of the function f1(x) = -8x?
Strictly decreasing everywhere
At which point does the function f2(x) = x² - 6x + 42 have a strict global minimum?
x = 3
What is the nature of the function f3(x) = x³ - 243x?
Strictly increasing on certain intervals and decreasing on others
What is the nature of the function f4(x) = x³ + 3x² + 3x + 100?
Strictly increasing everywhere
What is the nature of the function f5(x) = -3x⁴ - 32x³ - 90x²?
Strictly decreasing everywhere
What is the purpose of finding the derivative of a function in optimization problems?
To find the point where the function changes from increasing to decreasing
What is the characteristic of function f3 on the interval (−∞, −1]?
Strictly concave down
At what point is the function f5 not defined?
x = 8
What is the profit-maximizing quantity for the function P(q)?
q = 100
What is the characteristic of function f8 on the interval (−∞, 1)?
Strictly concave up
What is the revenue function R(q) in the profit maximization problem?
R(q) = 42q - 0.015q²
What is the condition for profit maximization in the problem?
C'(q) = R'(q)
This quiz covers finding local and global maxima and minima of functions, including polynomial and exponential functions. It involves determining the behavior of functions on different intervals and identifying maximum and minimum locations.
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