47.7k views
2 votes
If 1/10 < x < 1, for what value of x is the value of 10 + 1/x greatest?

Help quick pleaseee

2 Answers

2 votes

Final answer:

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.

User Gabriel Santos
by
7.5k points
3 votes

Answer:

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.

User Everzet
by
7.4k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories