SOLUTION: Somebody help me with this question please. Thank you! 3. Use the graph of the combined function 𝑦 = 2^𝑥 − 𝑥^2 to determine an approximate solution to the inequality

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Question 1162542: Somebody help me with this question please. Thank you!
3. Use the graph of the combined function 𝑦 = 2^𝑥 − 𝑥^2 to determine an approximate solution to the inequality 2^𝑥 > 𝑥^2.

Found 2 solutions by solver91311, ikleyn:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


The zeros of the function tell you where . The intervals where give you the intervals where .

Find the three zeros by inspection (-0.8 is close enough for the irrational one) which gives you four intervals. Pick a value that is not close to the endpoint of each interval (choose the smallest integer in the interval) and calculate the value of the function. If you get a positive result, then that interval is where . Or just do this part by inspection as well -- if the graph is above the -axis, that interval is part of the solution set of the inequality. You should end up with the union of two disjoint intervals.


John

My calculator said it, I believe it, that settles it


Answer by ikleyn(52832)   (Show Source): You can put this solution on YOUR website!
.

Go to this link

https://www.desmos.com/calculator

It is free of charge online calculator and plotting tool.

Input the formula 2^x - x^2 and look into this plot.

Find and learn useful setup options in this tool.

Play with it and have fan (!)


By the way, from the plot, you can see two integer solutions x= 2 and x= 4.

You can check it manually, that these integer values of x are valid solutions to the equation.

The third solution, close to x= -0.8, is not integer.



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