Apps of calculus q's... (1 Viewer)

[Kyroth***]

Hey,
I've got some questions I can't do, they're really bugging me. If anyone could tell me how, I'd really appreciate it.

1) Find the domain over which the equation is increasing.
y = x3 + 12x2 + 45x - 30
so I found y' and made it greater than 0, and came up with
3(x+5)(x+3)>0
and I don't know how to simplify from there.


2) Find the stationary points.
(3x-1)(x-2)4
So again, I found y' and made it = 0, and ended up with
15x4 + 44x3 + 192x2 - 96x + 32 = 0
And, again, I don't know how to find x.

3. Find the stationary points.
y = x(square root sign)(x+1) (ie, x, times the sqare root of x+1)
And again, I found y', and didn't know where to go. For simplicities sake, I won't try and type it out.

So, any help, please?

 

[acmilan]

1. 3(x+5)(x+3)>0

You set the left hand side = 0 and get x = -3 and x = -5

Now the LHS is just a parabola, so you have to see where that parabola is strictly greater than 0, this occurs at x < -5 and x > -3

2. y = (3x-1)(x-2)⁴

y' = 3(x - 2)⁴ + 4(3x - 1)(x - 2)³
y' = (x - 2)³[3(x - 2) + 4(3x - 1)] = (x - 2)³[15x - 10]

Thats much easier to solve now

 

[acmilan]

3. y = xsqrt(x + 1)

y' = sqrt(x + 1) + x/2sqrt(x + 1)

make y' = 0

sqrt(x + 1) + x/2sqrt(x + 1) = 0

2(x + 1) + x = 0
3x + 2 = 0

and so forth