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hoe to work out stationary points on the curve y x^1/2 + 1/(x^1/2)

Hey so i have this question:
Find any stationary points on the following curves and determine their nature.

(ii) y = square root(x) + 1/ square root (x)

so im really confused, i tried to differentiate it and got 0.5x1/2 - 0.5x-3/2

then i do 0.5x-1/2 (1-x3) = 0
and got x = 0 or x= +1

i tried to the whole table thing and i got 0 as a minimum and 1 as a maximum.

Have i done this correctly?
Original post by Appazap
Hey so i have this question:
Find any stationary points on the following curves and determine their nature.

(ii) y = square root(x) + 1/ square root (x)

so im really confused, i tried to differentiate it and got 0.5x1/2 - 0.5x-3/2

In red, should be -1/2. Typo, I presume, judging by the following.



then i do 0.5x-1/2 (1-x3) = 0


Try multiplying that out - you don't end up with your previous formula.

PS: function is not defined at x=0
Original post by Appazap
Hey so i have this question:
Find any stationary points on the following curves and determine their nature.

(ii) y = square root(x) + 1/ square root (x)

so im really confused, i tried to differentiate it and got 0.5x1/2 - 0.5x-3/2

then i do 0.5x-1/2 (1-x3) = 0
and got x = 0 or x= +1

i tried to the whole table thing and i got 0 as a minimum and 1 as a maximum.

Have i done this correctly?


Differential should be 12x−1/2−12x−3/2\frac{1}{2}x^{-1/2}-\frac{1}{2}x^{-3/2} so you made a small slip
Reply 3
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Appazap
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Original post by RDKGames
Differential should be 12x−1/2−12x−3/2\frac{1}{2}x^{-1/2}-\frac{1}{2}x^{-3/2} so you made a small slip


oh i see, how do i find x from this formulae?
Reply 4
Avatar for Appazap
Appazap
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Original post by ghostwalker


In red, should be -1/2. Typo, I presume, judging by the following.



Try multiplying that out - you don't end up with your previous formula.

PS: function is not defined at x=0

oh yeah should it be 0.5x-1/2(1-something) right?
Remember (x^n)(x^m) = x^(n+m).
Reply 6
Avatar for Appazap
Appazap
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16
Original post by TimGB
Remember (x^n)(x^m) = x^(n+m).


but im not multiplying the x's im adding them
Original post by Appazap
oh i see, how do i find x from this formulae?


Make it equal 0 and and solve for it. Then check whether the points are maxima/minima via second order differential.

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