Homework Set 8: Problem 10 Section 4.1, Problem 10 Section 4.2
Section 4.2: Problem 10 pg. 180
For f(x) = x3 -18x2 -10x +6, find the inflection point algebraically. Graph the function with a calculator or computer and confirm your answer.
(For the exponents, it is x cubed and -18x squared).

Need help with this homework problem. See attached file.
Please write complete, formal and professional proofs for your answer.
Also, please publish response as a Word or PDF file.
Infinite thanks!

Convert this SQL statement into relational algebra:
SELECT COUNT(*)
FROM Employees e1,e2, Department d
WHERE e1.lName = 'Adams' AND e1.fName = 'James' AND
e1.empID = d.mgrEmpID AND d.deptNo = e2.deptNo;

Please help me learn how to write these two proofs correctly for my Modern Algebra class.
Please submit all work as either a PDF or MS Word file.
** Please see the attached file for the complete problem description **

Let f : X -> Y be any function. Let sigma (Y ) be a sigma-algebra on Y .
Show that
{f −1 (B ) : B E sigma (Y )}
is a sigma-algebra on X. f −1 (B ) is the inverse image of B , that is
{x : f (x) E B }.
Where E represents the 'belongs to' symbol.

Suppose X is a measurable space, E belongs to the sigma algebra ( I believe to the sigma algebra in X) , let us consider X\E = Y. Show that all sets B which can be expressed as A\E, where A belongs to the sigma algebra in X, form a sigma-algebra in Y.
Please justify every step and claim you make in the solution.

What type of Algebra problems covered in an Algebra 1 course do you find to be the most challenging? Why? What did you learn from the experience of an Algebra 1 course and how did you overcome this challenge? If you could provide some tips or advice to new Algebra 1 students, what would you share with them?

Please see the attached file for full problem description with proper symbols.
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Let A be a sigma-algebra on Omega, and let B be an element of A. We denote A|B = A intersection B A E A.
1. Prove that A|B is a sigma-algebra on B.
2. Is is still true if B is not in A? Please prove the answer.

1. Very rarely do people use algebra in their jobs or their lives. At most, people use arithmetic. If this is the case then why do you suppose it is that we study algebra in the first place?