7. information about a function f(x) is given in the table.\n|x|−∞<x≤−3|x = −3|−3≤x≤5|x = 5|5≤x<∞|\n|f(x)|dec…
7. information about a function f(x) is given in the table.\n|x|−∞<x≤−3|x = −3|−3≤x≤5|x = 5|5≤x<∞|\n|f(x)|decreasing|5|increasing|11|increasing|\na. for which value(s) of x , if any, does f(x) have a relative (local) minimum?\nb. for which value(s) of x, if any, does f(x) have a relative (local) maximum?\n8. 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?\na) the value of the stock was at its absolute highest in 2019.\nb) the value of the stock reached a relative maximum in 2019.\nc) the value of the stock reached a relative minimum in 2017.\nd) the value of the stock was at its absolute lowest in june of 2020.
Answer
Explanation:
Step1: Recall the definition of relative minimum
A function has a relative minimum at a point where the function changes from decreasing to increasing. For (y = f(x)), from the table, (f(x)) is decreasing for (-\infty<x\leq - 3) and increasing for (-3\leq x\leq5). So (x=-3) is a relative - minimum point.
Step2: Recall the definition of relative maximum
A function has a relative maximum at a point where the function changes from increasing to decreasing. Since the function (f(x)) is increasing for (-3\leq x\leq5) and increasing for (5\leq x<\infty), there is no such point where the function changes from increasing to decreasing, so there is no relative maximum.
Step3: Analyze the stock - value problem
For the stock - value problem, the value of the stock increased from 2017 to 2019, then decreased until June 2020, and then increased again. A relative maximum occurs when the function (stock value as a function of time) changes from increasing to decreasing. So the stock value reached a relative maximum in 2019.
Answer:
a. (x = - 3) b. None 8. B. The value of the stock reached a relative maximum in 2019.