What is the maximum value of y if y = x^4 - 8x?

Answer 1

Poorly worded question, since there is no maximum value of y = x^4 - 8x

http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E4+-+8x

suppose we blindly proceed as usual ...

dy/dx = 4x^3 - 8
= 0 for a max/min
4x^3 = 8
x^3 = 2
x = 2^(1/3) = appr 1.2599
subbing that in gives us y = appr -7.56 as seen on the graph

using the 2nd derivative test:
y '' = 12x^2 - 8
subbing in x = 2^(1/3) gives a positive, so we are dealing with a minimum, not a maximum