How do you solve 4^x+4>=214x+421 using a graph?

1 Answer
Mar 8, 2017

Solution is x>=2.04371x2.04371

Explanation:

To solve 4^x+4>=214x+421 using a graph, first let us create a graph by choosing different values of xx say -11, -1/212, 00, 1/212, 11, 3/232, 22, 5/252, 33 and corresponding values of 4^x+44x+4.

These are ((-1,-1/2,0,1/2,1,3/2,2,5/2,3),(17/4,9/2,5,6,8,12,20,36,68))

and graph appears as follows:
graph{4^x+4 [-1, 3, -5, 30]}

As is observed by zooming the graph near the place, where 4^x+4 crosses y=21 and we find that 4^x+4>=21 for some x greater than 2, say around 2.04.

graph{4^x+4 [1.68, 2.18, 16.944, 21.32]}

Actually solution is x>=2.04371 (using MSExcel - Goal seek).