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Find the maximum value of (x^4-x^2)/(x^6+2x^3-1).

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CBSE/Class 12/Science/Mathematics Tuition/Class XI-XII Tuition (PUC)

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Tutor

Apply maxima minima concept separately for f(x) and g(x), you ll get the solution to be 0
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Tutor

The function will not have global maxima as the function value will go to infinity. However, at two different values of x, local maxima having value 1/6 is associated with this function. the corresponding values of x are (1/2 + (root(5))/2), (1/2 - (root(5))/2).
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Tutor

After solving it, you will get that the maxima will occur at (rt5+1)/2 and the maximum value will be 1/6.
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Tutor

Consider the question to be in the form f(x)/g(x). Now it is very clear it will be maximum only when f(x) is max. and g(x) is minimum. Apply maxima minima concept separately for f(x) and g(x), you ll get the solution to be 0
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0
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NumGeek

zero
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Excellence Award Winner

it will be 0
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Computer Wizard

It's around x = -0.555 which comes around 0.34
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0,1
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Maths Tutor

Are you sure there is a minus sign in the denominator?
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