Does the real rate depend on x? What does that tell you about the function?
Added by Cory R.
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The real rate typically refers to the interest rate that has been adjusted for inflation. It can be expressed as the nominal interest rate minus the inflation rate. Show more…
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Akash M.
Given that f is a real-valued differentiable function such that f(x)f(x')<0 for all real x, it follows that (a) f(x) is an increasing function (b) f(x) is a decreasing function (c) |f(x)| is an increasing function (d) |f(x)| is a decreasing function
Sri K.
$$ \begin{aligned} &F(x)=f(x)-\frac{\sqrt{3} x^{2}}{2} \\ &F^{\prime}(x)=f^{\prime}(x)-\sqrt{3} x \\ &\text { Now, } g(x)=f(x)-x \\ &g^{\prime}(x)=f^{\prime}(x)-1>0 \\ &\text { As } h(x)=f(x)-x^{3} \\ &\begin{aligned} h^{\prime}(x) &=f^{\prime}(x)-3 x^{2} \\ &=f^{\prime}(x)-3 x^{2}>0 \end{aligned} \end{aligned} $$ Now, for $x \in R, \sqrt{3} x<1$ or $3 x^{2}$ Hence $f^{\prime}(x)-\sqrt{3} x>0$ Hence, $\mathrm{A}$ is correct.
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