A curve has the equation $y = \frac{2x^2}{x + 2}$. Obtain expressions for \(\frac{\mathrm{d}y

Question

A curve has the equation $y = \frac{2x^2}{x + 2}$. Obtain expressions for $\frac{\mathrm{d}y}{\mathrm{d}x}$ and $\frac{\mathrm{d}^2y}{\mathrm{d}x^2}$ in the simplest form. Hence find, respectively, the range of values of $x$ for which $y$ is increasing and decreasing with respect to $x$.

Accepted Answer

(i) $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{2x(x+4)}{(x+2)^2},\ \dfrac{\mathrm{d}^2y}{\mathrm{d}x^2}=\dfrac{16}{(x+2)^3}$ (ii) Increasing for $x0$; decreasing for $-4<x<0$

Techniques of Differentiation - Second and Higher Derivatives

Techniques of Differentiation - Second and Higher Derivatives

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