This isn't quite homework, but still stuff I don't understand.
1- f(x) = 4x^2
0 < x ≤ 8
I understand that there's no local max, and that the absolute max is 256. But for local and absolute minimums I don't quite understand. How to find the min values. If I find the critical value and don't include 0, then there's no critical value, which means I don't understand how to find the mins.
Same thing with this one:
g(t) = | 4t - 9 |
g'(t) is 4. Which, as far as I know, doesn't mean there's a critical point.
One more question:
x^(-4)*ln(x)
Product rule. Right. But isn't the derivative of the left hand function x^(-4)*ln(-4), which doesn't exist because you can't take the log of a negative number?
For the first, does no absolute min imply that there's no local min?
What am I missing on the second derivative? The derivative of 4t is 4, the derivative of 9 is 0, no?
For the third one, could you show me your steps? I did this: (I was backwards in my first post)
F(x) = x^(-4)*ln(x)
f(x) = x^(-4)
f'(x) = -4x^(-5)
g(x) = ln(x)
g'(x) = 1/x
F'(x) = f'(x)g(x) + f(x)g'(x)
F'(x) = -4x^(-5) * ln(x) +