Find the rate of change

- anonymous

Find the rate of change

- jamiebookeater

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- anonymous

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- anonymous

ummm

- anonymous

let me try

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- anonymous

okk

- anonymous

answer choice?

- anonymous

@aloud can you help me out?

- anonymous

it's not any answer choices

- anonymous

kind in a tight situation

- anonymous

i have to go in couple min

- anonymous

lol ya ik me to

- anonymous

@H3LPN33DED help plz?

- anonymous

- anonymous

sorry dianolove idk this one i am only in geometry

- anonymous

it's okk

- anonymous

(1,2) (2,3)

- anonymous

- anonymous

@aloud, that would be an approximation of the rate of change

- anonymous

however, at the point (2,3) -tangent to curve you would have an exact rate of change

- anonymous

so the rate of change is (2,3)

- anonymous

The way to solve this exercise is to first find the equation of the parabola, followed by the derivative of it and for that you will have to choose a particular x - value.

- anonymous

like (2,1)

- anonymous

What aboyt the reverse, @Hoslos , if you know the derivative at a point, can you integrate to find original function?

- anonymous

Let us find the equation of the parabola, using the formula:
\[y=a(x-p)^{2}+q\], where x,y is from any coordinate of the graph and p and q are the x and y - values of the vertex, respectively.
The first attempt is to find a . Replacing values, we get:
\[1=a(1-3)^{2}+2\]
\[1=a(-2)^{2}+2\]
\[1-2=4a\]
\[a=-0.25\]
Next we re-write the equation, by now putting a and the vertex coordinates, giving us:
\[y=-0.25(x-3)^{2} +2\]

- anonymous

Well, the rate of change will have to end at the derivative, which will mean the change in y with respect to x, @BPDlkeme234 .

- anonymous

i'm sorry this is just hard

- anonymous

As for the second part, you differentiate the equation of the formula:
\[\frac{ d _{y} }{ d _{x} }= -0.5(x-3)\]
There it is. Depending on the question, they would tell you a particular value of x runing in the graph.
For instance let us say, when the x-value is 2. The rate of change will be \[-0.5(2-3)=0.5units/time\]
Any question on differentiation, please ask.

- anonymous

thanks for tryin i still dont get it but thanks

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