Question

Given f'(x)=(x-4)(6-2x) find the x-coordinate for the relative minimum of the graph f(x).
OPTIONS:
8
6
3
None of these

I think it is 3, but I am also conflicted to say none of these because I graphed the function and ant see a minimum.

Answer 1

*cant

Answer 2

clearly it is either 3 or 4.
Since 4 is not a choice, 3 seems logical.

Now, knowing what you do about cubic curves, and that this one comes down from the left, its first turnaround will be a minimum. So, it will be at x=3.

Or, note that f" = -4x+14.
f"(3) = 2 > 0, so f(3) is a minimum.

I can't see how you could have graphed it and not seen a minimum.