Question

Use calculus to locate the stationary points on the graph y=x+2/x

Answer 1

I have located the x values of sqrt(2) and -sqrt(2) but i cannot solve that back into y=x+2x

Answer 2

you got the right, what is the question?

Answer 3

I cannot solve the x values into the original equation to find the y coordinates

Answer 4

For the first one i have f'(sqrt(2))=Sqrt(2) + 2/sqrt(2)

Answer 5

oh ok we can do that

Answer 6

\[f(\sqrt2)=\sqrt2+\frac{2}{\sqrt{2}}=\sqrt{2}+\sqrt{2}=2\sqrt{2}\]

Answer 7

How did you just get rid of the numerator 2 so easily

Answer 8

same for the other one, except it is negative

Answer 9

it is always the case that \(\frac{a}{\sqrt{a}}=\sqrt{a}\)

Answer 10

How is that? I have never learnt that before?

Answer 11

rationalize the denominator, and you will see it instantly

Answer 12

but it is \[\sqrt{2} + 2/\sqrt{2}\]

Answer 13

or if you prefer, show
\[\left(\frac{a}{\sqrt{a}}\right)^2=a\]

Answer 14

yeah right

Answer 15

and since \(\frac{2}{\sqrt{2}}=\sqrt{2}\) you get
\[\sqrt{2}+\sqrt{2}=2\sqrt{2}\]

Answer 16

How is sqrt(2) + sqrt(2) = 2*sqrt(2)

Answer 17

oh bugger its like terms. sorry im not thinking

Answer 18

Sorry, thanks for the help mate, i think i get it now

Answer 19

yw

Answer 20

Have a good one :)