i thought the answer would be -1 but i dont know if i did it wrong or not cuz itz not in the answer choice. .?

Question

http://i181.photobucket.com/albums/x85/ctti_3/untitled-21.jpg

Answer 1

-1 is the x-value that gives the absolute max value of -17/8.

The absolute maximum is -1... but...
The absolute maximum value is -17/8 .... also...
The absolute maximum point is (-1, -17/8).

If you are asked for the value, you give the y-value.


d:

Answer 2

f(x) = 2(x - 1/(16x^2)) = 2x - x^(-2) / 8
f'(x) = 2 - (1/8)(-2)x^(-3) = 2 + (1/4)(1/x^3)
= 0 when 1/x^3 = -8
=> x^3 = -1/8
=> x = -1/2.
f"(x) = (1/4)(-3)x^(-4) = -(3/4) (1/x^4)
This is negative for all x ≠ 0, so there is a maximum at x = -1/2. So there are no critical points on (-∞, -1] and the function is increasing everywhere on this interval. So the absolute maximum will be at x = -1.
f(-1) = 2(-1 - 1/16) = -17/8.