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Multiple Choice Quiz
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1
Like linear programs, nonlinear programs will have a maximization or minimization objective function.
A)True
B)False
2
A necessary condition for a one variable decision problem with an objective function, which is continuous, is that the first derivative of the function be 0 at a local maximum or minimum point.
A)True
B)False
3
Necessary and sufficient conditions for the existence of a local maximum in a single variable unconstrained nonlinear optimization problem is that the first derivative be 0 at a point and the second derivative be negative at the same point.
A)True
B)False
4
Necessary and sufficient conditions for the existence of a local minimum in a single variable unconstrained nonlinear optimization problem is the second derivative be negative at a point and at the same point the slope of the function be 0.
A)True
B)False
5
In general global maximums value of the objective function of unconstrained nonlinear optimization problems will be greater than all local maximums.
A)True
B)False
6
The local minimum of a convex function will also be the global minimum.
A)True
B)False
7
Partial derivatives are used to find extreme values of decision variables in a nonlinear model with 2 or more variables.
A)True
B)False
8
The local minimum for the function 2 X2 – 4 X – 3 is obtained when x is equal to:
A)1
B)2
C)3
D)4
9
The local maximum for the function f(X) = 8 X3 + 2 X2 – 4 X – 3 is obtained when X is equal to:
A)1.
B)–1.
C)5/6.
D)2.
10
The value of the function f(X) = 4 X3 + 2 X2 – 4 X – 10 at its local maximum is:
A)–8.
B)8.
C)1
D)–1.
11
For the function f(X) = 6 X2 +12 X + 30, the slope of the function is 0 at X equal to:
A)6.
B)12.
C)3 .
D)–1.
12
If the slope of the function f(X) = 4 X2 -24 X + 32, is 0 at X=3, then it follows that x=3 is a
A)local maximum.
B)local minimum.
C)global maximum.
D)saddle point.





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