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

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Sujoy Das

JU-IITKGP & 10+ years experienced for boards, JEE,NEET,OLYMPIAD & 5-12

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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An Engineer

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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Tutor

0
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Computer Wizard

It's around x = -0.555 which comes around 0.34
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Maths Tutor for the last 15 years - an IIT Engineer with 22 years' experience in the IT Industry

Are you sure there is a minus sign in the denominator?
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perspicacious, physicist, rationalist

for finding maxima u need to do by finding the derivative and look for x which give its minimum value in denominator, And the answer is 0
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NumGeek

zero
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Excellence Award Winner ( 7 times )

it will be 0
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