The diagram shows a curve with equation $$$y=4 x^{\frac{1}{2}}-2 x$$$ for $$$x \geqslant 0$$$, and a straight line with equation $$$y=3-x$$$. The curve crosses the $$$x$$$-axis at $$$A(4,0)$$$ and crosses the straight line at $$$B$$$ and $$$C$$$. Show that $$$B$$$ is a stationary point on the curve. .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... .................................................................................................................................................... ....................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w20_qp_11 Year：2020 Question No：12(b)

Answer:

$\frac{\mathrm{d} y}{\mathrm{~d} x}=2 x^{1 / 2}-2$
$\frac{\mathrm{d} y}{\mathrm{~d} x}$ or $2 x^{1 / 2}-2=0$ when $x=1$ hence $B$ is a stationary point

Knowledge points:

1.7.4 locate stationary points and determine their nature, and use information about stationary points in sketching graphs. (Including use of the second derivative for identifying maxima and minima; alternatives may be used in questions where no method is specified.) (Knowledge of points of inflexion is not included.)

Answer:

Knowledge points:

Solution:

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