h As x takes on every value from x2 to x8 which of the follo

h.) As x takes on every value from x=2 to x=8, which of the following best describes the values of

?

They increase and then decrease.

They increase.    

They decrease

.They decrease and then increase.

Solution

The answer depends on f (x) which has not been stated. Any positive number, when divided by a number less than 1, increases in value. Similarly, any negative number, when divided by a number less than 1, decreases in value. Let us take a few simple examples:

i. Let f(x) = x. Then [ f (x + 0.1) - f (x)]/ 0.1 = [ x + 0.1 - x]/0.1 = 0.1/0.1 = 1 i.e it will remain constant regardless of the changes in value of x;

ii. Let f (x) = x²   .Then [ f (x + 0.1) - f (x)]/ 0.1 = [ ( x + 0.1)² - x²] / 0.1 =( 0 .2x + 0.01)/ 0.1. This will increse with increase in values of x from 2 to 8;

It s thus clear that the answer depends on f (x)