AP EAMCET2002MathematicsApplication of Derivatives

If (1+x)- 2 x 2+x is increasing, then

Options

A0 < x <
B- < x < 0
C- < x <
D-1 < x < 2

Correct answer

C. - < x <

Step-by-step solution

Let f(x)= (1+x)- 2 x 2+x^2 f^ (x)= 1 (1+x) - 2 2+x + 2 x (2+x)^2 For increasing function, f^ (x)>0 aligned (2+x)^2-2(2+x)(1+x)+2 x(1+x) & >0 4+x^2+4 x-4-6 x-2 x^2+2 x+2 x^2 & >0 x^2 & >0 aligned This shows x lies between - to .

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