Question

If 1/10 < x < 1, for what value of x is the value of 10 + 1/x greatest?

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Answer 1

The greatest value of the expression 10 + 1/x within the range 1/10 < x < 1 is obtained when x is just above 1/10.

Step-by-step explanation:

The student is asking for the value of x within the range 1/10 < x < 1 that will make the expression 10 + 1/x the greatest. To maximize the value of 10 + 1/x, we need to maximize the value of 1/x, which occurs when x is as small as possible within the given range. Since x can be any value greater than 1/10 and less than 1, the value of x that will make 1/x the greatest is infinitesimally more than 1/10.

Answer 2

Step-by-step explanation:

We can safely focus on 1/x. The smaller x is, the greater 1/x will be. Note that x cannot equal zero. Here we are asked to focus on 1/10 < x < 1, in which 1/10 is obviously the smallest x value. But 1/10 < x < 1 restricts x to numbers greater than 1/10. The graph of y = 10 + 1/x is not defined for x = 1/10, but as we approach x = 1/10 along the graph, we see the graph approaching (but not touching) the maximum value 10 + 1/(1/10), or 20.