The parametric equations of a curve are $$\[ x=t+\ln (t+2), \quad y=(t-1) \mathrm{e}^{-2 t}, \]$$ where $$$t>-2$$$. Find the exact $$$y$$$-coordinate of the stationary point of the curve. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s21_qp_33 Year：2021 Question No：3(b)

Answer:

Equate derivative to zero and solve for $t$
Obtain $t=\frac{3}{2}$ and obtain answer $y=\frac{1}{2} \mathrm{e}^{-3}$, or exact equivalent

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.)

3.4.3 find and use the first derivative of a function which is defined parametrically or implicitly.

Answer:

Knowledge points:

Solution:

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