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!
Thanks a lot!
Sep 23rd 2009, 11:54 PM
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=8-k.
Sep 24th 2009, 08:31 AM
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...
Sep 24th 2009, 08:39 AM
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.