Graphing (1 Viewer)

[Lukybear]

How to graph this from scratch?

y=x(3+sqrtx)

Do we have to know the general form of it?

 

[Cazic]

You know what the graph for sqrt(x) looks like, right? Well, this thing will be the same basic shape, just increasing quicker.

To get your bearings for this one as opposed to sqrt(x), this thing still starts at (0,0), but passes through (1, 4) and (4, 20) instead of (1,1) and (4, 2). Same shape but.

 

[lychnobity]

How to graph this from scratch?

y=x(3+sqrtx)

Do we have to know the general form of it?

No, just know how to do it. ie process

Use multiplication

1) Draw
2) Draw x
3) Multiply the ordinates

 

[Tofuu]

no, just know how to do it. Ie process

use multiplication

1) draw
2) draw x
3) multiply the ordinates

+1

 

[Cazic]

Better to just get a feel for how multiplying by 'x' changes a graph imo. Doing it pointwise like that without a feeling might be time consuming for no reason.

 

[The Nomad]

You can draw 3 + x^0.5, then to get x(3 + x^0.5): add an x-intercept at x = 0.

 

[khorne]

use this information to sketch the graph and imo, multiplication/addition/etc of ordinates should be avoided at all costs. too inaccurate/tiresome

Use this method.

 

[SeCKSiiMiNh]

If all else fails, you could always just plot it the good old fashion way

 

[Cazic]

Use this method.

I don't see why.

The derivative is undefined at x = 0 because the function is undefined for x < 0, but that doesn't mean there is going to be a vertical tangent there. In fact, given the derivative he listed, my guess is the function has a tangent line whose slope is very close to 3 when you're very close to 0.

Analysing the function a bit more, a function is concave down on some region if the derivative is decreasing (not the same as negative) on that region. But the derivative is clearly increasing on any region the function is defined on (the square root function in the first derivative is an increasing function "by memory", or consider that the second derivative is always positive). So it's actually concave up.

 

[untouchablecuz]

I don't see why.

The derivative is undefined at x = 0 because the function is undefined for x < 0, but that doesn't mean there is going to be a vertical tangent there. In fact, given the derivative he listed, my guess is the function has a tangent line whose slope is very close to 3 when you're very close to 0.

Analysing the function a bit more, a function is concave down on some region if the derivative is decreasing (not the same as negative) on that region. But the derivative is clearly increasing on any region the function is defined on (the square root function in the first derivative is an increasing function "by memory", or consider that the second derivative is always positive). So it's actually concave up.

you are correct

i quickly assumed a vertical tangent without taking limits

thanks

 

[Lukybear]

I don't see why.

The derivative is undefined at x = 0 because the function is undefined for x < 0, but that doesn't mean there is going to be a vertical tangent there. In fact, given the derivative he listed, my guess is the function has a tangent line whose slope is very close to 3 when you're very close to 0.

Analysing the function a bit more, a function is concave down on some region if the derivative is decreasing (not the same as negative) on that region. But the derivative is clearly increasing on any region the function is defined on (the square root function in the first derivative is an increasing function "by memory", or consider that the second derivative is always positive). So it's actually concave up.

One question that i have is why is the vertical tangent always stated, even it isnt really relevant to question.

Also how would we formalise this solution?

 

[untouchablecuz]

ok this is def. correct

 

[GUSSSSSSSSSSSSS]

why shud multiplication of ordinates be avoided at all costs untouchablecuz???
i found its very quick to get the shape of the curve and then with a little testing you can find out the exact points that are necessary

..

 

[khorne]

I don't see why.

The method outlined is correct, although the working for the question isn't.