Thread: Local Extrema Question

Problem: Find values of a and b so that the function has a local maximum at the point (6, 18).





How do I solve this? Could you show your steps so I can see what you're doing and why? Also, how do you solve it to be a local maximum or minimum? I don't understand the concept of this problem at all, much less this specific problem.


EDIT: I found the value of b by taking the derivative of the original equation, which is:



Then I solved for a:



I plugged that back into the original derivative, set it equal to 0, and solved for b, getting , which is correct.

However, I can't figure out how to solve for a now! I keep getting an answer of 0, which I know isn't right!

Originally Posted by lysserloo

Problem: Find values of a and b so that the function has a local maximum at the point (6, 18).





How do I solve this? Could you show your steps so I can see what you're doing and why?

So far, I've taken the derivative and found the critical point, which I think is . That's all I've done, and I don't think it's right.

First we know that



Now if we take the derivative we know that when becuase it is a maximum.


so we have



So one of the two above factors must be zero. We will choose the 2nd one (why?)

from above now we know that



So

I've gotten as far as solving for b; I just edited my original post.

How did you get 3e for a? That's the only part I'm stuck on now. Solving for a.

EDIT: Ope! I understand! Never mind.

[size=3]Hello, lysserloo!['/size]

Find values of and so that the function has a local maximum at the point (6, 18).

. .

Your work is correct!


The derivative is: .
. . So the critical value is: .

But we are told that the maximum is at (6, 18) . . . That is,

. . So we have: .

The function (so far) is: .


The point (6, 18) tells us that: .

So we have: .

. . Got it?

Oh wow, that explanation was PERFECT. Thank you SO much, it's much more clear now!