dy/dx = -4/x^2 + sec^2 (πx/8) (π/8)
= 0 for a max/min
π/(8cos^2 (πx/8)) = 4/x^2
8cos^2 (πx/8) /π = x^2/4
cos^2 (πx/8) = πx^2/32
there is no simple way to solve,
I ran it through Wolfram's amazing equation solver and got
x = ± 2.13448
http://www.wolframalpha.com/input/?i=cos%5E2+%28πx%2F8%29+%3D+πx%5E2%2F32
arrghhh, after all that, our solution is ouside the domain, so simply
if x=1
y = 4/1 + tan(π/8) = 4.414
if x = 2
y = 4/2 + tan(π/4) = 2+1 = 3
look at the graph of
http://www.wolframalpha.com/input/?i=y+%3D+4%2Fx+%2B+tan%28πx%2F8%29
everything makes sense.
Locate the absolute extrema of the function on the closed interval:
y= 4/x+tan(pix/8), [1,2]
1 answer
2 answers