Posted by **Matt** on Monday, November 13, 2006 at 8:17pm.

Great! I understand now that

C0=f(a)

c1=f'(a)

c2=f"(a)/2

Now, If I am to find the parabolization of the equation x^2-x at x=2, then

c0=x^2-x=2^2-2=2

c1=2x-1=2(2)-1=3

c2=2/2=1

So, the equation (taken from c0+c1(x-a)+c2(x-a)^2) is >>

2+3(x-2)+1(x-2)^2??

Is this correct?

Thanks

In calc, we are studying parabolization. It is the linerazation of a parabola. The linerazation of a standard line is L(x) = b0+b1(x-a) when f(x) is at x=a

b0 = f(a)

b1=f'(a)

The parabolization of f(x) at x=a is given by the equation

P(x)=c0+c1(x-a)+c2(x-a)^2.

f(a) = P(a)

F'(a) = P'(a)

f''(a) = P''(a)

I need to find a formula for c0, c1, and c2 in terms of f(a), f'(a) and f"(a)

Im sure that I need to find the first and second derivitive of the equation c0+c1(x-a)+c2(x-a)^2. Im just not sure where to start...

Thanks!

Matt

Actually, linearization is approxiamtion by a straight line while Parabolization is approximation of a function by a parabola.

You start from:

f(a) = P(a)

f'(a) = P'(a)

f''(a) = P''(a)

Then you insert

P(x)=c0+c1(x-a)+c2(x-a)^2

in here.

So,

P(a) = C0

P'(x) = C1+2c2(x-a) --->

P'(a) = C1

P''(x) = 2C2 -->

P''(a) = 2C2

This means that:

f(a) = P(a) = C0

f'(a) = P'(a) = C1

f''(a) = P''(a) = 2C2

And it follows that:

P(x) = C0+C1(x-a)+c2(x-a)^2 =

f(a) + f'(a)(x-a) + f''(a)/2 (x-a)^2

There is an easy way to check. If you parabolize a parabola, you should get the same thing back. So, let's see:

2+3(x-2)+ (x-2)^2 =

2 + 3x-6 + (x^2 - 4x + 4) =

2-6+4 + 3x-4x + x^2 =

x^2 - x.

So, it's indeed the same!

## Answer This Question

## Related Questions

- Calculus - Solve the differential equation dy/dx = -xe^y and determine the ...
- drwls, is this correct,math - drawls this is from the previous post is this ...
- Algebra 2 - I have a question and I can not figure it out. Any answers to the ...
- calculus - what is the derivative? - Let f(x) = 2x^2 + 1 a. Find the derivative ...
- math - I need help with this question. Write the equation of the line which ...
- Calculus - I am unsure of how to take the derivative of this equation. It may be...
- Calculus - Find the scalar equation of the plane through the points M(1,2,3) and...
- correction of math - can someone correct this for me please. Directions: Solve ...
- Pre Cal.--Check my work? - Solve the system of equations: x - y - z = 2; x + 2y...
- Math - 2x represents that Clyde is twice (2 times) as old as Bonnie. 6 years ...

More Related Questions