A minimum from two exponential terms

A minimum from two exponential terms

Secondary 4
6 marks
TGM Original Questions

A curve has equation \(y=e^{2x}-8e^x+3\), where \(x\) is real.

  1. Find the exact coordinates of the stationary point.[3]
  2. Determine its nature using the second derivative test.[2]
  3. State the interval on which the function is decreasing.[1]

Solution:

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Answer:(a) \((\ln4,-13)\). (b) Minimum. (c) \(x<\ln4\).

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