The equation of a curve is $$$y=54 x-(2 x-7)^{3}$$$. Find the coordinates of each of the stationary points on the curve. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_12 Year：2020 Question No：10(b)

Answer:

$\frac{\mathrm{d} y}{\mathrm{~d} x}=0 \rightarrow(2 x-7)^{2}=9$
$x=5, y=243$ or $x=2, y=135$

Knowledge points:

1.1.3 solve quadratic equations, and quadratic inequalities, in one unknown (By factorising, completing the square and using the formula.)

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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