Asked by rita s
the curve c has equation y=x^2-1nx, x>0. Show that c has just 1 turning point and find its cordinates.
Answers
Answered by
Steve
1 turning point means that y'=0 at only one place, and y"≠0 there
y' = 2x-1/x
y" = 2+1/x^2
Note that y">0 for all x.
y'=0 where
2x^2-1 = 0
x = ±1/√2
But lnx is undefined for x<=0, so y'=0 only at 1/√2
y' = 2x-1/x
y" = 2+1/x^2
Note that y">0 for all x.
y'=0 where
2x^2-1 = 0
x = ±1/√2
But lnx is undefined for x<=0, so y'=0 only at 1/√2