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Someone help me solve this please watch

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    I'm trying to do question 7 in exercise 8K in the blue C3 book. How do I solve it to find the range of values? The equation above is a differential of a function. I'm trying to find the range of values for which f(x) is an increasing function of x. How do I solve it?
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    Is that (i)  \frac{12}{x} - \frac{3}{2\sqrt{x}} >0 or (ii)  \frac{12}{x} - \frac{3}{2}\sqrt{x} >0

    In both cases take the term with the square root to the right hand side by addition/subtraction and square the whole inequality (which should be justified, I guess x > 0 is a restriction right? It should be for a C3 problem).

    If you can't work out what to do next try this:
    Spoiler:
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    You then end up with something like  \frac{144}{x^2} > \frac{9}{4x} \ \text{or} \ \frac{9}{4}x . Multiply the  x^2 across and solve like a typical inequality with polynomials (consider different cases for x if necessary).
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    (Original post by benwellsday)
    Is that (i)  \frac{12}{x} - \frac{3}{2\sqrt{x}} >0 or (ii)  \frac{12}{x} - \frac{3}{2}\sqrt{x} >0

    In both cases take the term with the square root to the right hand side by addition/subtraction and square the whole inequality (which should be justified, I guess x > 0 is a restriction right? It should be for a C3 problem).

    If you can't work out what to do next try this:
    Spoiler:
    Show

    You then end up with something like  \frac{144}{x^2} > \frac{9}{4x} \ \text{or} \ \frac{9}{4}x . Multiply the  x^2 across and solve like a typical inequality with polynomials (consider different cases for x if necessary).

    Ah I get it now thanks
 
 
 
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Updated: January 17, 2010

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