Question

The graph below shows a company's profit f(x), in dollars, depending on the price of erasers x, in dollars, being sold by the company:

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?

Part B: If at one time the profit of the company was at least $120 what domain could possibly produce this profit?

Part C: What is an approximate average rate of change of the graph from x = 1 to x = 4, and what does this rate represent?

Answer 1

This is what I have for Part A: Part A: The x-intercepts represent the prices when no prices were made and the maximum value represents the highest profit. The price increases until x = 4. Then the prices decreases when x is greater than 4.

Is that correct??

Answer 2

@TheSmartOne

Answer 3

@radar

Answer 4

That appears to be right for Part A.

Answer 5

for part B the profit minimum of 120 dollars is when the price x = 1
the domain would be 1 to 6 (1,6)

Answer 6

Ok so would it be 1 is greater than or equal to x which is less than or equal to 6?

Answer 7

sorry - the profit is 120 dallars for x = 7

so domain is (1,7)

Answer 8

so would it be 1 is greater than or equal to x which is less than or equal to 7

Answer 9

yes

Answer 10

ok thanks so much! For part c the rate of change would be 50 but what does it represent

Answer 11

i should have written it as [1,7]
but what you wrote is fine.

Answer 12

ok thanks! What about C?

Answer 13

like what does it represent?

Answer 14

@welshfella

Answer 15

i guess its the average increase of profit per unit increase of price of erasers.

Answer 16

ok thanks so much! @welshfella do you think you could help me with another question?

Answer 17

A sandbag was thrown downward from a building. The function f(t) = -16t2 - 32t + 384 shows the height f(t), in feet, of the sandbag after t seconds:

Part A: Factor the function f(t) and use the factors to interpret the meaning of the x-intercept of the function.

Part B: Complete the square of the expression for f(x) to determine the vertex of the graph of f(x). Would this be a maximum or minimum on the graph?

Part C: Use your answer in part B to determine the axis of symmetry for f(x)?

@welshfella

Answer 18

can you post it separately please

Answer 19

ok sure!