Thread: Extrema help

Hi, after a long break I've decided to look at my math hw since I go back to school tomorrow. Well, I don't understand the first problem so hopefully if I can get help with this one I can understand the rest.

1. (noncalculator) The minimum value of f(x) = x^4 - 4x^3 + k is 7. Determine the value of k

I know how to find min and max values, but this is different so all help is appreciated.

Thanks

You know that for some fix value of x. What you need to determine is first the value of x when the function has its minimum value, i.e. when . Plug that value of x into the equation above and you'll get k.

Don't forget to test your critical values obtained from f'(x) = 0. Perhaps the easiest way is to check concavity using f''(x).

Originally Posted by Ridley

You know that for some fix value of x. What you need to determine is first the value of x when the function has its minimum value, i.e. when . Plug that value of x into the equation above and you'll get k.

Hi, I'm just confused with how I'm supposed to determine the value of x when the function has its min value, for, I have a "k" in the equation which prohibits me from determining x

k is a constant...what happens to it when you differentiate?

k merely serves to vertically translate the function, does this affect the instantaneous slope?

Originally Posted by MarkFL2

k is a constant...what happens to it when you differentiate?

k merely serves to vertically translate the function, does this affect the instantaneous slope?

Oh... completely forgot about that, so if k is a constant then the first derivative is simply 4x^3 -12x^2, and when I set that equal to zero I get x=3 and x=0

I now test to see which value of x gives the min by plugging into the equation of second derivative which is: 12x^2 - 24x

when i plug both of these values into the equation of second derivative i get a value of 0 for when i plug in 0 and a value of 36 when i plug in 3, since 36 is positive it indicates concave up which indicates a min, thus x=3 must be my value for x

I then plug 3 into x for original equation and for k I get -20

does this sound correct??

All of it is good except for finding k.

Originally Posted by MarkFL2

All of it is good except for finding k.

Oh yeah thanks for catching me on that, I merely got k - 27 = 7 and instead of doing 27+7 I did -27+7, thanks for all the help!

Glad to help!