Let . If is decreasing in then…

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

Let f(x)=x(ex−e−x)−2x−∫(ex−e−x) dxf(x) = x(e^x - e^{-x}) - 2x - \int (e^x - e^{-x})\,dx. If f(x)f(x) is decreasing in (x1,x2)(x_1, x_2) then (x1+x2)(x_1 + x_2) equals (a) 0 (b) 2e2e (c) e2−1e\frac{e^2 - 1}{e} (d) 32e\frac{3}{2}e

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