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!
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.
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!