Question

7 The diagram shows the curve \( y=x \mathrm{e}^{2 x}-5 x \) and its minimum point \( M \), where \( x=\alpha \). (a) Show that \( \alpha \) satisfies the equation \( \alpha=\frac{1}{2} \ln \left(\frac{5}{1+2 \alpha}\right) \). [3] (b) Verify by calculation that \( \alpha \) lies between 0.4 and 0.5 . \( [2] \) (c) Use an iterative formula based on the equation in part (a) to determine \( \alpha \) correct to 2 decimal places. Give the result of each iteration to 4 decimal places. [3]

          7

The diagram shows the curve \( y=x \mathrm{e}^{2 x}-5 x \) and its minimum point \( M \), where \( x=\alpha \).
(a) Show that \( \alpha \) satisfies the equation \( \alpha=\frac{1}{2} \ln \left(\frac{5}{1+2 \alpha}\right) \).
[3]
(b) Verify by calculation that \( \alpha \) lies between 0.4 and 0.5 .
\( [2] \)
(c) Use an iterative formula based on the equation in part (a) to determine \( \alpha \) correct to 2 decimal places. Give the result of each iteration to 4 decimal places.
[3]

7

The diagram shows the curve y=x e^2 x-5 x and its minimum point M, where x=α.
(a) Show that α satisfies the equation α=(1)/(2)ln((5)/(1+2 α)).
[3]
(b) Verify by calculation that α lies between 0.4 and 0.5 .
[2]
(c) Use an iterative formula based on the equation in part (a) to determine α correct to 2 decimal places. Give the result of each iteration to 4 decimal places.
[3]

Added by Nicholas N.

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