Wat zou dit voor een soort functie zijn?:-)

Nog meer maffe grafieken

• Desmos

Opening of asymptoot?

\( \eqalign{f(x) = \frac{{x^3 - 2x^2 - x + 2}} {{x^2 - 4x + 4}}} \)

Nagekomen bericht:-)

\( \begin{array}{l} y'' - y' - 2y = 0 \\ y( - 1) = 1 \\ y(1) = 0 \\ k^2 - k - 2 = 0 \\ (k - 2)(k + 1) = 0 \\ k = 2 \vee k = - 1 \\ y = C_1 \cdot e^{2x} + C_2 \cdot e^{ - x} \\ \left\{ \begin{array}{l} C_1 \cdot e^{ - 2} + C_2 \cdot e = 1 \\ C_1 \cdot e^2 + C_2 \cdot e^{ - 1} = 0 \\ \end{array} \right. \\ \left\{ \begin{array}{l} C_1 = \frac{{e^2 }}{{1 - e^6 }} \\ C_2 = \frac{{e^5 }}{{e^6 - 1}} \\ \end{array} \right. \\ y = \frac{{e^2 }}{{1 - e^6 }} \cdot e^{2x} + \frac{{e^5 }}{{e^6 - 1}} \cdot e^{ - x} \\ y = - \frac{{e^2 }}{{e^6 - 1}} \cdot e^{2x} + \frac{{e^5 }}{{e^6 - 1}} \cdot e^{ - x} \\ y = \frac{{e^{5 - x} - e^{2x + 2} }}{{e^6 - 1}} \\ \end{array} \)

The milkmaid problem

"It's milking time at the farm, and the milkmaid has been sent to the field to get the day's milk. She's in a hurry to get back for a date with a handsome young goatherd, so she wants to finish her job as quickly as possible. However, before she can gather the milk, she has to rinse out her bucket in the nearby river.

Just when she reaches point M, our heroine spots the cow, way down at point C. Because she is in a hurry, she wants to take the shortest possible path from where she is to the river and then to the cow. So what is the best point P on the riverbank for her to rinse the bucket?"

An Introduction to Lagrange Multipliers

Dat is ook toevallig

Schema: maxima, minima en zadelpunten