Question

1. information about a function $f(x)$ is given in the table.

$\

$$\begin{array}{c|c|c|c|c|c}x&-\\infty < x < - 3&x = - 3&-3 < x \\leq 5&x = 5&5 \\leq x < \\infty\\\f(x)&\\text{decreasing}&5&\\text{increasing}&11&\\text{increasing}\\end{array}$$

$
a. for which value(s) of $x$, if any, does $f(x)$ have a relative (local) minimum?
b. for which value(s) of $x$, if any, does $f(x)$ have a relative (local) maximum?

1. the value of stock in chelseas chocolate company increased between 2017 and 2019, then decreased until june of 2020, then started increasing again. which of the following conclusions is true?

a) the value of the stock was at its absolute highest in 2019.
b) the value of the stock reached a relative maximum in 2019.
c) the value of the stock reached a relative minimum in 2017.
d) the value of the stock was at its absolute lowest in june of 2020.

Explanation:

Step1: Recall relative - minimum concept

A function $f(x)$ has a relative minimum at a point $x = c$ if $f(x)$ is decreasing to the left of $c$ and increasing to the right of $c$.

Step2: Analyze the table for part a

For the function $f(x)$, it is decreasing for $-\infty

Step3: Recall relative - maximum concept

A function $f(x)$ has a relative maximum at a point $x = c$ if $f(x)$ is increasing to the left of $c$ and decreasing to the right of $c$.

Step4: Analyze the table for part b

The function $f(x)$ is increasing for $-3

Step5: Analyze stock - value problem (question 8)

The value of the stock increased between 2017 and 2019, then decreased until June 2020, then increased again. A relative maximum occurs when the function changes from increasing to decreasing. So, the value of the stock reached a relative maximum in 2019.

Answer:

a. $x = - 3$
b. None

1. B. The value of the stock reached a relative maximum in 2019.