# Thread: Problem with question! (exponential)

1. ## Problem with question! (exponential)

(a) Let $y=15x^\frac{3}{2}-x^\frac{5}{2}$ . Find the set of values of x for which y is decreasing, showing your method clearly.

(b) It is given that $f(x)=e^{ax}-ax-1$ , where a is a positive constant. Show that f is an increasing function for x>0.

How do i approach these 2 questions? Thank you!

2. ## Re: Problem with question! (exponential)

Originally Posted by pumbaa213
(a) Let $y=15x^\frac{3}{2}-x^\frac{5}{2}$ . Find the set of values of x for which y is decreasing, showing your method clearly.

(b) It is given that $f(x)=e^{ax}-ax-1$ , where a is a positive constant. Show that f is an increasing function for x>0.
You posted this question in the basic algebra forum.
However, it really requires simple calculus to give a rigorous solution. Use the derivatives.

If you cannot use calculus, then the best you can do is to look at each graph.

3. ## Re: Problem with question! (exponential)

The function will be decreasing for x > 9
We have to involve calculus for the solution of this question. steps are the same
find first derivative equate that to zero to get critical points. we get zero and nine.
The function is not defined for values of x < 0.
By careful examination and reasoning we conclude that the function is increasing for 0 <=x <9. and it is decreasing for x >9

4. ## Re: Problem with question! (exponential)

Thanks for the help guys!