A curve is defined by the equation $y = \ln \left( \frac{\mathrm{e}^x}{x^2 + 10} \right)$. Show th

Question

A curve is defined by the equation $y = \ln \left( \frac{\mathrm{e}^x}{x^2 + 10} \right)$. Show that the curve has no turning points for all real values of $x$.[5]

Accepted Answer

$\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{(x-1)^2+9}{x^2+10}>0$ for all real $x$, so the curve has no turning points.

CGSS PRELIMS P1 Q6

CGSS PRELIMS P1 Q6

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