Question

Determine where f(x)= (x-x^2) / (1+8x^2) is increasing and decreasing.

Answer 1

did you find f'(x) ?

Answer 2

Yes I did

Answer 3

Not sure about the increasing part though

Answer 4

cool you can look at where it is positive and negative...
where it is positive, f(x) is increasing... where it is negative f(x) is decreasing

Answer 5

Can you give an example ?

Answer 6

I have f'(x)

Answer 7

I'd recommend you plot it, the numbers look a little rough to be doing algebra, but just as a rough sketch... the denom. is always positive so... look at the numerator...

Answer 8

-8*x^2 -2*x +1

Answer 9

that's going to be negative for most x; the only time it will be positive is when
1> 8*x^2 +2*x

Answer 10

ie for small values of x ... you could actually solve that for the roots.... and then you'd know where it will be positive... because you have already determined that it will look something like: (roughly)

Answer 11

is that clear?

Answer 12

So it is possible to do it algebraically though right? With f'(x)

Answer 13

I'm looking it over... seems messy, so I'm guessing they want you to do it with a calc. ...?

Answer 14

Yeah I just plugged it in