Thread: Find function with these minimums and maximums

Find values of a,b,c and d such that g(x) = ax^3+bx^2+cx+d has a local maximum of (2,4) and a local minimum at (0,0).

How do I do this?

Originally Posted by theowne

Find values of a,b,c and d such that g(x) = ax^3+bx^2+cx+d has a local maximum of (2,4) and a local minimum at (0,0).

How do I do this?

You know four things ....haha and two more ...and

Yes, that is the question...and what to do from there to find the original equation?

Originally Posted by theowne

Yes, that is the question...and what to do from there to find the original equation?

...hmm four equations with four variables...hmm that sounds solvable...hmm...set it up =D haha...

Set what up? What four equations? The only equations I can see involved are the function, derivative and second derivative. I am attempting to learn this material, it'd be more helpful to see an example to learn from.

Originally Posted by theowne

Set what up? What four equations? The only equations I can see involved are the function, derivative and second derivative. I am attempting to learn this material, it'd be more helpful to see an example to learn from.

...we know that ...therfore ...now you also know that ...so ...now that you get the jist..set up your other equations and solve for the coefficents

Originally Posted by theowne

Find values of a,b,c and d such that g(x) = ax^3+bx^2+cx+d has a local maximum of (2,4) and a local minimum at (0,0).

How do I do this?

With the above info we get

using the point (0,0)





since we know that c=d=0 we get



using the point (2,4)





solving this system by substition (or elimination)



so then b=3

Finally we get