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?
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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??
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That appears to be right for Part A.
for part B the profit minimum of 120 dollars is when the price x = 1
the domain would be 1 to 6 (1,6)
Ok so would it be 1 is greater than or equal to x which is less than or equal to 6?
sorry - the profit is 120 dallars for x = 7
so domain is (1,7)
so would it be 1 is greater than or equal to x which is less than or equal to 7
ok thanks so much! For part c the rate of change would be 50 but what does it represent
i should have written it as [1,7]
but what you wrote is fine.
ok thanks! What about C?
like what does it represent?
i guess its the average increase of profit per unit increase of price of erasers.
ok thanks so much! @welshfella do you think you could help me with another question?
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)?