
cubic polynomial...
Hello,
I need a help here in this problem...
For f(x) = x^3 + 6x^2  15x + k, the absolute maximum and absolute minimum value on the interval [10, 2] have the same absolute value. Find the value of K? ....
I know we need to find the first derivative and then set them equal to zero but then I am stuck getting some absolute maximum as (100+K) and absolute minimum as (250+k)...and if they are equal...it just does not make any sense!
Please help!
Thanks a lot!

The first derivative equals 0 at 5 and 1. It's easy to check that at 5 is maximum and at 1 minimum. The value of this extremes are 100 +k and 8 +k.
If their absolute value are equal, their signs have to be different. So 100+k=8k.

thanks for the help Sir!
I get the value of K as 46...
But how come 250+k is not the choice? when we plug the 10 as one of the end points we get (250+k)....
please let me know if I am wrong...

At 1 is local minimum and it is 8+k.
At 10 is global minimum and it is 250+k.
At 5 there is local and global maximum and it's 100+k.
So if gloabl maximum and minium had the same absolute value the answer would be k=75.
And if local maximum and minium had the same absolute value the answer would be k=46.