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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.