Question 934068
Integrate,
{{{dy/dx=x^(1/2)-x^(-1/2)}}}
{{{y=(2/3)x^(3/2)+2x^(1/2)+C}}}
Use the point to solve for {{{C}}}
{{{2/3=(2/3)4^(3/2)+2*4^(1/2)+C}}}
{{{2/3=(2/3)8+4+C}}}
{{{C=-26/3}}}
{{{highlight(y=(2/3)x^(3/2)+2x^(1/2)-26/3)}}}
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{{{d(dy/dx)/dx=(1/2)x^(-1/2)+(1/2)x^(-3/2)}}}
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{{{graph(300,300,-10,10,-10,10,(2/3)x^(3/2)+2x^(1/2)-26/3)}}}