Find the exact coordinates of the stationary point on the curve with equation $$$y=5 x \mathrm{e}^{\frac{1}{2} x}$$$. ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................ ................................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_22 Year：2020 Question No：2

Answer:

Differentiate using product rule to obtain $a \mathrm{e}^{\frac{1}{2} x}+b x \mathrm{e}^{\frac{1}{2} x}$
Obtain correct $5 \mathrm{e}^{\frac{1}{2} x}+\frac{5}{2} x \mathrm{e}^{\frac{1}{2} x} \mathrm{OE}$
Equate first derivative to zero and solve for $x$
Obtain $x$-coordinate $-2$
Obtain $y$-coordinate $-10 \mathrm{e}^{-1}$

Knowledge points:

2.4.1 use the derivatives of ,ln x,sin x,cos x,tan x, together with constant multiples, sums, differences and composites

Answer:

Knowledge points:

Solution:

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