An exponential product with a maximum

An exponential product with a maximum

Secondary 4
5 marks
TGM Original Questions

A curve has equation \(y=(x+1)e^{-x}\), where \(x\) is real.

  1. Find \(\frac{\mathrm{d}y}{\mathrm{d}x}\).[2]
  2. Find the coordinates and nature of the stationary point.[3]

Solution:

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Answer:(a) \(-xe^{-x}\). (b) Maximum at \((0,1)\).

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