Question

I am asked to verify if this function is decreasing or increasing:

f(x)=sqrt(2+5x)

I am using Maple 15 right now in my class and writing the following commands can’t solve the problem.

f := x-> sqrt(2+5*x):
solve(diff(f(x), x) > 0, x);

After Run; it is shown to me that :

Warning, solutions may have been lost

In fact, I expect to have some intervals, but it isn’t done properly. What can I do? Thanks for any help!

Answer 1

The domain of sqrt(2+5*x) is all points x such that 2+5*x is not less than zero.

For this example, you can ask Maple whether it can tell that the derivative of sqrt(2+5*x) is greater than zero for all x in the domain. If the answer is true then it is increasing everywhere in its domain.

restart:

is( diff(sqrt(2+5*x),x) > 0 ) assuming 2+5*x >= 0;

                          true