Thread: A quick question about Increasing and decreasing Functions.

Ok so it says here

A manufacturing company finds the profit for a production level of x motors per hour is

p = 400 x sqr(12x - x^2) - 100 x e (0,12]
For what range of production is the profit
Increasing
Decreasing


Now the answer is (0, 6) increasing and (6, 12) decreasing.

When I found the derivative, I got

(-200x +2400) (12x-x^2)^-1/2

Now the critical number for the first bracket is 12, which I found, makes sence because the function decreases at 12. But I cant find where the 6 comes from.

Can anyone help?

Originally Posted by Sky12

Ok so it says here

A manufacturing company finds the profit for a production level of x motors per hour is

p = 400 x sqr(12x - x^2) - 100 x e (0,12]
For what range of production is the profit
Increasing
Decreasing

Thus you have,

And I assume you mean,

So find the derivative und make it zero.

Thus,

Multiply through by the radical,

Divide by 200,




Thus,

But,
.
Thus,

Is the only solution.

Now take any point to the left of 9 (and more than zero) and see what the sign is. Positive increasing and negative decreasing. Same for any point to the right of 9 (and less than 12)

Ah sorry for the confusion but i ment the x as (times) so it would be more like

400sqr(12x - x^2) - 100