polynomial with derivative (1 Viewer)

juantheron

Active Member
Joined
Feb 9, 2012
Messages
259
Gender
Male
HSC
N/A
Let be a real polynomials of Least Degree Which has Local Maximum at and Local Minimum


at .If and . Then
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
The polynomial of least degree having 2 distinct local max/min points is a cubic polynomial, which can be generalised to become:



We will now use the details that they gave us to find the values of a, b, c and d:

Local maximum at x=1:



Local minimum at x=3:



(1) - (2) to eliminate 'c' gives us:



Now we use P(1) = 6:



Similarly for P(3) = 2:



Solve simultaneously to find the value of 'c' because that is the value that P'(0) takes ie:

 

juantheron

Active Member
Joined
Feb 9, 2012
Messages
259
Gender
Male
HSC
N/A
Thanks Carrotsticks , after seeing Your Solution, I get This Method



and from your equation i also get

So Is my solution is Right OR Not

Thanks
 

Carrotsticks

Retired
Joined
Jun 29, 2009
Messages
9,494
Gender
Undisclosed
HSC
N/A
I'm not going to check your arithmetic, but your method is right!
 

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

Top