Use the graph of the combined function y=3^3 - x^3 - 1 below to determine an approximate solution to inequality 3^x < x^3 + 1
see the related (actually, identical) question below, at
https://www.jiskha.com/questions/1829682/use-the-graph-of-the-combined-function-y-3-x-x-3-1-to-determine-an-approximate
To determine an approximate solution to the inequality 3^x < x^3 + 1 using the given graph of the combined function y = 3^3 - x^3 - 1, you can follow these steps:
Step 1: Identify the points where the graph of the function y = 3^3 - x^3 - 1 intersects the x-axis. These points represent the solutions to the equation 3^x = x^3 + 1.
Step 2: Draw a horizontal line y = 0 (which represents the x-axis) on the graph, and note the x-values where the graph intersects this line.
Step 3: Examine the behavior of the function on each side of the identified x-values. Determine whether the function is positive (+) or negative (-) in those regions.
Step 4: Based on the sign of the function in each region, determine the regions where 3^x < x^3 + 1. These will be the regions where the function is negative (-).
Step 5: Estimate the x-values that fall within the regions identified in Step 4.
Please note that this method provides only approximate solutions and is based on visual inspection of the graph. For a more accurate solution, you may need to utilize numerical or algebraic methods.