Final answer:
To graph the cubic function for 0≤ x ≤ 10, plot points and connect them. The turning points occur where the slope changes from positive to negative. The graph suggests fluctuating oil prices that don't rise indefinitely.
Step-by-step explanation:
To graph the function f(x) = 0.2728x^3 - 2.612x^2 + 7.02x + 89.18 for 0 ≤ x ≤ 10, we can plot several points and connect them to create a smooth curve. Here are the steps:
1. Choose different values of x within the given range (0 to 10).
2. Substitute each value of x into the function to find the corresponding y-value.
3. Plot the points (x, y) on a coordinate plane.
4. Connect the plotted points to create a smooth curve.
The turning points of the graph, also known as the local extrema, occur where the slope of the function changes from positive to negative or vice versa. These points can be found by taking the derivative of the function, setting it equal to zero, and solving for x. The end behavior of the graph can be determined by examining the leading term of the function, which in this case is 0.2728x^3. As x approaches positive or negative infinity, the function grows without bound.
The graph suggests that crude oil prices initially decrease, then increase, and finally level off over time. This means that the price of crude oil is likely to fluctuate, but in the long run, it does not continue to rise indefinitely. Historical events and market factors, such as shifts in supply and demand, can influence the trends in crude oil prices.
It is not reasonable to assume that the trend will continue indefinitely. As mentioned earlier, crude oil prices are influenced by various factors, and they tend to fluctuate over time. Additionally, technological advancements, alternative energy sources, and changes in market dynamics can also affect the long-term trend in crude oil prices.