CAIE IGCSE Additional Math 14.6 stationary points

Use this stationary-points page to differentiate polynomial, exponential or composite curves, solve dy/dx=0 and substitute roots into y.

Exam points

Find dy/dx and solve dy/dx=0 to locate all stationary x-coordinates on a curve.
Substitute stationary x-values back into y to find exact coordinate pairs.
Solve factored or surd equations that arise from stationary-point conditions.

[Maximum number: 3]

The equation of a curve is $y=kxe^{-2x}$ , where k is a constant.

Find the coordinates of the stationary point on the curve $y=10xe^{-2x}$ .

Equate $\frac{dy}{dx}=0$ and find
10-20x=0
M1
$\left(\frac{1}{2},\frac{5}{e}\right)$
A2; A1 for $x=\frac{1}{2}$ only. Equivalent $y=5e^{-1}$ or decimal 1.84 accepted.

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14.6. Find stationary points question 1