How Derivatives Affect the Shape of a Graph 7

Question

Consider the function 𝑓(𝑥)=8𝑥+7𝑥-1. For this function there are four important intervals: (-∞,𝐴], [𝐴,𝐵),(𝐵,𝐶], and [𝐶,∞) where 𝐴, and 𝐶 are the critical numbers and the function is not defined at 𝐵.

Find 𝐴   

and 𝐵   

and 𝐶   

For each of the following open intervals, tell whether 𝑓(𝑥) is increasing or decreasing.

(-∞,𝐴): Select an answer Increasing Decreasing 

(𝐴,𝐵): Select an answer Increasing Decreasing 

(𝐵,𝐶): Select an answer Increasing Decreasing 

(𝐶,∞) Select an answer Increasing Decreasing 

Note that this function has no inflection points, but we can still consider its concavity. For each of the following intervals, tell whether 𝑓(𝑥) is concave up or concave down.

(-∞,𝐵): Select an answer Concave Up Concave Down 

(𝐵,∞): Select an answer Concave Up Concave Down 

Answer 1

Here's what the student was probably trying to ask.

Answer 2

The function given is linear. It does not have a maximum or a minimum.