Question

a local minimum of a function is its

a) largest value of the function over its entire domain.
b) smallest value of the function over its entire domain.
c) largest value for a given interval.
d) smallest value for a given interval.

question 10 (5 points)
multiply the polynomials: \\((x - 4)(x^2 + 2x - 5)\\)

a) \\(x^3 - 2x^2 - 13x + 20\\)
b) \\(x^3 + 6x^2 + 3x - 20\\)
c) \\(x^3 + 6x^2 + 3x + 20\\)
d) \\(x^3 - 2x^2 - 13x - 20\\)

question 11 (5 points)
multiply: \\((x + 3)(x^2 + x - 2)\\)

a) \\(x^2 + x - 6\\)
b) \\(x^3 + 3x^2 - 2x - 6\\)
c) \\(x^3 + 4x^2 + x - 6\\)
d) \\(x^2 - x - 6\\)

Explanation:

Define local minimum

Using the Relative Extrema knowledge point
A local minimum is the smallest value that a function takes on within a given neighborhood or interval, rather than over its entire domain.

Multiply first polynomial set

To multiply \((x - 4)(x^2 + 2x - 5)\), we distribute each term in the first polynomial to each term in the second polynomial:

$$
LATEXBLOCK0
$$

Multiply second polynomial set

To multiply \((x + 3)(x^2 + x - 2)\), we distribute each term in the first polynomial to each term in the second polynomial:

$$
LATEXBLOCK1
$$

Answer:

Question 1

• (A) largest value of the function over its entire domain.
• (B) smallest value of the function over its entire domain.
• (C) largest value for a given interval.
• (D) smallest value for a given interval. (Correct answer)

Question 10

• (A) \(x^3 - 2x^2 - 13x + 20\) (Correct answer)
• (B) \(x^3 + 6x^2 + 3x - 20\)
• (C) \(x^3 + 6x^2 + 3x + 20\)
• (D) \(x^3 - 2x^2 - 13x - 20\)

Question 11

• (A) \(x^2 + x - 6\)
• (B) \(x^3 + 3x^2 - 2x - 6\)
• (C) \(x^3 + 4x^2 + x - 6\) (Correct answer)
• (D) \(x^2 - x - 6\)