- where A,B, and C are constants $$f(x)=Ax^2+Bx+C$$
(c) What are the sign restrictions on A, B and C for f(x) to attain a minimum value?
(d) What are the sign restrictions on A, B and C for f(x) to attain a maximum value?
2026-04-05 14:54:09.1775400849
Minimum, Maximum, and extreme points
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Answer these 20 questions, true or false and give a reason. That is all the question is asking.
1) If $A$ is positive $Ax^2 + Bx + C$ will always have a maximum. True or False.
2) If $A$ is positive $Ax^2 + Bx + C$ will always have a minimum. True or False.
3) If $A$ is negative $Ax^2 + Bx + C$ may or may not have a maximum. True or False.
4) If $A$ is negative $Ax^2 + Bx + C$ may or may not have a minimum. True or False.
5) If $B$ is positive $Ax^2 + Bx + C$ will always have a maximum. True or False.
6) If $B$ is positive $Ax^2 + Bx + C$ will always have a minimum. True or False.
7) If $B$ is negative $Ax^2 + Bx + C$ may or may not have a maximum. True or False.
8) If $B$ is negative $Ax^2 + Bx + C$ may or may not have a minimum. True or False.
9) If $C$ is positive $Ax^2 + Bx + C$ will always have a maximum. True or False.
10) If $C$ is positive $Ax^2 + Bx + C$ will always have a minimum. True or False.
11) If $C$ is negative $Ax^2 + Bx + C$ may or may not have a maximum. True or False.
12) If $C$ is negative $Ax^2 + Bx + C$ may or may not have a minimum. True or False.
13) If $B$ is zero $Ax^2 + Bx + C$ will always have a maximum. True or False.
14) If $B$ is zero $Ax^2 + Bx + C$ will always have a minimum. True or False.
15) If $B$ is zero $Ax^2 + Bx + C$ may or may not have a maximum. True or False.
16) If $B$ is ero $Ax^2 + Bx + C$ may or may not have a minimum. True or False.
17) If $C$ is zero $Ax^2 + Bx + C$ will always have a maximum. True or False.
18) If $C$ is zero $Ax^2 + Bx + C$ will always have a minimum. True or False.
19) If $C$ is zero $Ax^2 + Bx + C$ may or may not have a maximum. True or False.
20) If $C$ is zero $Ax^2 + Bx + C$ may or may not have a minimum. True or False.