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UPSC NDA I 2016 Mathematics Solved Paper

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For the next two (2)items that follow :

Consider the function

f(x)=\frac{27(x^{2/3}-x)}{4}

[NDA I 2016]

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Question : 15 of 120

Marks: +1, -0

How many solution does the function

f(x)=-1

One
Two
Three
Four

Solution:

f(x)=\;\;\frac{27}{4}(x^{2/3}-x)

=\;\;\frac{27}{4}((x^{2})^{1/3}-x)

Similarly for

f(x)=-1

we will get

27y^{3}-27y^{2}-4=0

and after solving it we will find that it has two solution

y_0=1.1184,-0.05922

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