Thread: Increasing and Decreasing Functions

Hi, I am stuck on this problem, the instructions indicate to find the intervals of increase and decrease for the given function.

h(u) = square root of 9-u^2 The square root is over the entire term.

We were told to differentiate first, and then to factor to find the zeros. When I try to differentiate I am getting 3-(1/2)X^-(3/2) This doesn't look right so I need some clarification as to whether I am differentiating correctly.

BTW The final answer should be:

h(u) is increasing for -3< u < 0
h(u) is decreasing for 0< u < 3

Originally Posted by kdogg121

Hi, I am stuck on this problem, the instructions indicate to find the intervals of increase and decrease for the given function.

h(u) = square root of 9-u^2 The square root is over the entire term.

We were told to differentiate first, and then to factor to find the zeros. When I try to differentiate I am getting 3-(1/2)X^-(3/2) This doesn't look right so I need some clarification as to whether I am differentiating correctly.

BTW The final answer should be:

h(u) is increasing for -3< u < 0
h(u) is decreasing for 0< u < 3

.

From the chain rule:

where I've used the index laws and .

Important note: h(u) is only defined for .....

So was I correct then? 3-(1/2)U^-(1/2) is the derivative?

Will this factor?

Originally Posted by kdogg121

So was I correct then? 3-(1/2)U^-(1/2) is the derivative?

Unfortunately not, no.

Are you familiar with the chain rule? Here it is:



This theorem should be memorized, if you haven't already. So, applying it here, we can see the benefits. Our initial function:



Let

Then:



Can you finish it up?

Originally Posted by kdogg121

So was I correct then? 3-(1/2)U^-(1/2) is the derivative?

Will this factor?

Sorry, but I can't see how either of the answers you've come up with are the same as the correct answer (see my first reply) of

.

The solution to is clearly u = 0, obtained by setting the numerator equal to zero. The factoring business you mentioned is completely irrelevant .......

Therefore:

1. when u > 0 AND (recall the important note from my earlier reply and also look at where is undefined), that is, .

2. when yada yada

I figured it out with the chain rule finally, thanks guys.