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secondary 4 | A Maths

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The dy/dx path is going on an incorrect track in my opinion since dy/dx = 0 simply tells us to find the turning points.

3a² + 5a - 2 = 0

(3a + 1) (a - 2) = 0

a = -1/3, a = 2

e^x = -1/3, e^x = 2

We know that any positive number, raised to any real power, will be positive and can therefore not equal -1/3.

We will only have one solution arising from e^x = 2, and that is x = ln 2 = 0.69314... ~ 0.69.