JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q72

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MathematicsSingle correct+4 / -1Question 72 of 90

Let k and K be the minimum and the maximum values of the function $f(x)=\dfrac{(1+x)^{0.6}}{1+x^{0.6}}$ in [0, 1] respectively, then the ordered pair (k, K) is equal to :

(1,2^{0.6})

(2^{-0.4},2^{0.6})

(2^{-0.6},1)

(2^{-0.4},1)

Answer and worked solution

Official answer: D

$\dfrac{f'}f=\dfrac{0.6}{1+x}-\dfrac{0.6x^{-0.4}}{1+x^{0.6}}$ , whose sign is that of $(1+x^{0.6})-x^{-0.4}(1+x)=1-x^{-0.4}\le0$ on $(0,1]$ . So $f$ decreases: $K=f(0)=1$ and $k=f(1)=\dfrac{2^{0.6}}2=2^{-0.4}$ .

Topics:Monotonicity

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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 72