18x^4+11x^2+4x+8

What is the maximum^?

No maximum; see explanation

Step-by-step explanation:

The easiest way to find the maximum value of this polynomial is to graph it. If you are not allowed to graph it, then the next easiest way to find the maximum would be to use calculus (if you can't use calculus I'll explain how to do that way as well).

Graphing:

Use a free graphing calculator online or a personal graphing calculator. You will see that this function has no maximum and continues upward forever. If you are interested in other methods to determine this they are below.

Using Calculus:

1. Find the derivative of the polynomial:

72x^3+22x+4

2. Set the derivative = 0 and solve for all solutions:

72x^3+22x+4 = 0

0 = 2(6x+1)(6x^2-x+2)

0 = (6x+1)(6x^2-x+2)

0 = (6x+1)                 Important equation 1

0 = (6x^2-x+2)         Important equation 2

So x = -1/6 because 6x^2-x+2 has no solution

(This step produces critical points that you should test values near)

3. Test one point larger than -1/6 and one smaller than -1/6 by plugging them into the derivative:

Point 1: -2

Point 2: 0

72(-2)^3+22(-2)+4 = -616

72(0)^3+22(0)+4 = 4

Since the smaller term is negative and the larger term is positive x=-1/6 is a minimum value for this polynomial. Since only one x-value was found with the derivative test, this function has no maximum (it is technically infinity).

Without Calculus:

1. Set the polynomial = 0 and simplify:

18x^4+11x^2+4x+8 = 0

No simplification can happen.

(This step would give points that you should test values close to).

2. Test points

Plug points into the polynomial to get an understanding of the shape of the graph.

x=0 y=8;

x=1 y=41;

x=10 y=181148;

x=-100000000 (approximately negative infinity) y = approximately infinity

x=1000000000 (approximately positive infinity) y = approximately infinity

Based on the tested points, this graph has no maximum, it continues upward forever.

answer:   segregation violated the equal protection clause of the 14th amendment, which holds that no state can “deny to any person within its jurisdiction the equal protection of the laws.”

details/explanation:

brown v. board of education of topeka, decided by the us supreme court in 1954, ruled that all americans are entitled to the same civil liberties and protections in regard to access to education. until that decision, it was legal to segregate schools according to race, so that black students could not attend the same schools as white students.   an older supreme court decision, plessy v. ferguson (1896), had said that separate, segregated public facilities were acceptable as long as the facilities offered were equal in quality.   in the case of brown v. board of education, that standard was challenged and defeated.   segregation was shown to create inequality, and the supreme court unanimously ruled segregation to be unconstitutional.

the ruling was important in advancing civil rights because it affirmed that the 14th amendment applies to all rights and privileges of citizens, including access to   education.   this was being violated by states whose laws supported the segregation of schools.   section 1 of the 14th amendment reads as follows:

im not sure

step-by-step explanation: