I need to find a function that can be proved using calculus techniques. I have used every local source of information to find a method to work this out but alas... the answer eludes me.

 

Heres the question:

 

Following 5 point lie on a function: (1,20) (2,4) (5,3) (6,2) (10,1)

Find an equation that passes through these points and has all the following:

 

3 points of inflection

At least 1 local minimum and local maximum

At least one Critical point (eg max/min/intercept etc) is not at a given point

The curve is continuous and differentiable throughout

The equation is not a single polynomial, but must be a piecewise-defined function

 

Now I know that theres gonna be many different functions. All I need is a method to work one out for myself. I am at a loss of how im meant to get this...

 

Thanks for any help provided

 

Crozius

Looks like you and I have the same maths class

Lake Tuggers ?

 

Either way, I'm looking for the exact same question. So looks like we won't have unique functions Crozius .

 

For the first, pick the first three values and arbitrarily decide the derivative at the third point should be -1.

 

For the second, start on the other end and match the derivative, since the problem statement says it has to be differentiable everywhere.

 

Really, just pick some functions out of a hat and make them do what you want. The derivative of -1 was 100% arbitrary.

 

The starting place is a function with arbitrary coefficients. Then you solve for the coefficients that make it do what you want.

Edited May 31, 200817 yr by xceL

Plug that baby into a calculator.

If you can find me a calculator that can do that, I would be very surprised.

I'm probably reading far to much into this, but it looks like you want to do a polynomail fit, and decent maths package will do it...

 

Even some like excel (ewwwwwwwwwwww) http://facultystaff.richmond.edu/~cstevens/301/Excel4.html

 

If it where I I'd use R... http://www.r-project.org/

I use a TI-84 to find polynomials to fit through a bunch of random points all the time.

It won't satisfy all the requirements of the first post, though.

 

The equation is not a single polynomial, but must be a piecewise-defined function

He doesn't always have to go for the 'A'

All of that doesnt answer my question...

 

I use a TI-84 plus calculator and it doesnt give the graph that im expecting, nor does it have the qualities that is required.

 

Any method you guys can come up with that i can use on paper then check with the calculator would be better so i can show working.

 

Thanks.

 

Xcel yes, lake tuggers, which teacher you got?

So, here's my particular thought....

 

why not think a little outside the box.

 

You have several requirements here:

(A) goes through (1,20) (2,4) (5,3) (6,2) and (10,1)

(B) 3 points of inflection

© At least 1 local minimum and local maximum

(D) At least one Critical point (eg max/min/intercept etc) is not at a given point

(E) The curve is continuous and differentiable throughout

(F) The equation is not a single polynomial, but must be a piecewise-defined function

 

1) Fit a polynomial to go through those 6 points. This takes care of (A). Limit the polynomial to the range x=(0,11)

2) Then piecewise append functions in the negative quadrant of x, and x>11 to fulfill the other requirements.

 

That is, if you've written out the entire problem statement, there isn't a given limit on how much of x you can use. So, use the rest of [math] (-\infty,0)[/math] and [math](11,+\infty)[/math] Put the necessary points of inflection at x = 100,200,500. Or something like that. The only real difficulty here is to pick good functions at the piecewise breaks to fulfill the continuity and differentiability requirements.

Ms. R... something with an R.

Rietta? Yeh that's the one. Line 1 with rietta. lulz.

 

I already got an answer on another forum but it has like 9 decimal places LOL.

I'll have to use that. ;<

It's like 12.2203213983x + 52.1092312029^x + ln(x+5) + 44.210931^whatever lol.

Eitehr way i;x'm drunk at the moment and have no idea how to do the asisngment LOL!

gud luck!

Edited June 1, 200817 yr by xceL