Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (6 points)

Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (4 points)

Question

Part A: What do the x-intercepts and maximum value of the graph represent? What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit? (6 points)

Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (4 points)

angelcook2007 · Answer

attachment

mhanifa · Answer

First off, do you have any idea? Anything particularly you need help with?

angelcook2007 · Answer

@mhanifa wrote:

First off, do you have any idea? Anything particularly you need help with?

No idea

angelcook2007 · Answer

I've done something similar to this before and it had product on the bottom and profit in the y axis

mhanifa · Answer

This is similar

mhanifa · Answer

Do you remember how you solved that?

Florisalreadytaken · Answer

Part A: What do the x-intercepts and maximum value of the graph represent?

the profit this company makes is represented by $ f(x) $ right? that means where the lines intersect, that is going to be how much profit the company makes. in the image you attached, the $x$ intercepts are $0$, which means that they represent where this company's profit is $0$

the maximum value of the graph, so vertex represents the maximum profit the company makes by selling $3$ pens as you can see there in the $y$ axis, and $ 120$ $.

$\cdot$What are the intervals where the function is increasing and decreasing, and what do they represent about the sale and profit?

well, we can see where the parabola starts there at $0$ and finishes at $ 6 $, where 3 is the peak of it right? so we can say that if $0\leq x  \leq 3$ , then we have a profit increase, the left hand side, whilst on the right hand side we can see that if $3\leq x  \leq 6$ , we are going to have a profit decrease.

Part B: What is an approximate average rate of change of the graph from x = 3 to x = 5, and what does this rate represent? (4 points)

to figure that out we will be using this formula:
$$  \frac{y_2 -y_1}{  x_2-   x_1} $$
where 
$$  (x_1  , y_1) \Rightarrow (3 , y_1  )  \text{  and   }  (x_2  , y_2) \Rightarrow (5 , y_2  )    $$
to find the values of $ y_1  $ and $y_2$ you will have to look at the graph

after you find the values of both $ y$, then its pretty easy from there right?

angelcook2007 · Answer

@florisalreadytaken

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