derivative, and intervals of increase,decrease,extreme point

[RicH8sMath]

ok this is my first post so thanx in advance to anyone reading this.

This is concepts of calculus.

"find the intervals of increase, decrease, and extreme points"
f(x)= sqrt( x^2+4x )

i know first step is finding the derivative
so ... {(1/2)x^2 + 2x}^(-1/2)


from here i'm somewhat lost, how can i tell the points of increase decrease and extreme point
if i graph it looks like INCREASE (-infinity, 4)U(4, ???) and DECREASE (??, 0)U(0,infinity), i dont know where the extreme point is, but that is just me graphing it and looking at it, but mathematically am i supposed to set it equal to 0?? and if so what am i solving for? I'm a little lost and wondering if i'm on the right path.

thanx in advance.

 

[Dr. Flim-Flam]

f(x) = sqrt(x^2+4x), hence we know that x^2+4x >= 0, x(x+4) >=0,

----------------------------0++++++++++++++++++++++
-------------0+++++++++++++++++++++++++++++++++
-4 0

The above tells us that the domain of f(x) is (-Inf,-4} union {0, inf).

Can you take it from here?

 

[RicH8sMath]

dr. flimflam

that's the original formula

in the book it's telling me to take the first derivative so it would be

f'(x)= {(1/2)x^2 + 2x}^(-1/2) and that's where i get stuck and, how can i set that equal to zero


and just to make sure i got the procedure right

1. take the 1st derivative,
2. set it equal to 0
??

 

[Deleted member 4993]

dr. flimflam

that's the original formula

in the book it's telling me to take the first derivative so it would be

f'(x)= {(1/2)x^2 + 2x}^(-1/2) and that's where i get stuck and, how can i set that equal to zero


and just to make sure i got the procedure right

1. take the 1st derivative,
2. set it equal to 0 and points where undefined

That's the procedure (or part of the procedure) .

To find whether function is increasing or decreasing - after finding the critical points - you need to decide - the domains where the derivative is positive (function increasing) and where the derivative is negative, (function decreasing).

Remember - for derivative to from positive to negative - it must go through zero (or undefined region)
??

 

[Dr. Flim-Flam]

f(x) = sqrt(x^2+4x), f ' (x) = (x+2)/sqrt(x^2+4x) = m (the slope)

Setting the slope equal to zero, we have x = -2, however f(-2) = sqrt(-4), an imaginary number, hence, there isn't any

extrema on the real number line, unles you consider the range which is [0, inf).