The equation of a curve is $$$y \mathrm{e}^{2 x}-y^{2} \mathrm{e}^{x}=2$$$. Find the exact coordinates of the point on the curve where the tangent is parallel to the $$$y$$$-axis. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_w21_qp_32 Year：2021 Question No：9(b)

Answer:

Equate denominator to zero and substitute for $y$ or for $\mathrm{e}^{x}$ in the equation of the curve
Obtain equation of the form $a \mathrm{e}^{3 x}=b$ or $c y^{3}=d$
Obtain $x=\ln 2$
Obtain $y=1$

Knowledge points:

1.7.1 understand the gradient of a curve at a point as the limit of the gradients of a suitable sequence of chords, and use the notations for first and second derivatives (Only an informal understanding of the idea of a limit is expected.)

3.2.3 use logarithms to solve equations and inequalities in which the unknown appears in indices

Answer:

Knowledge points:

Solution:

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