For $0\le x\le \pi$ the function is $f(x)=e^{2x}\sin x$. (a) Find all values of $x$ in this interval where the tangent to the curve is horizontal. (b) State whether each such point is a local maximum, minimum or point of inflection.

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x = \pi - \arctan\left(\frac{1}{2}\right) (approximately 2.678); the point is a local maximum

Neco 2025 Further Mathematics Question 17

For \\(0\\le x\\le \\pi\\) the function is \\(f(x)=e^{2x}\sin x\\). (a) Find all values of \\(x\\) in this interval where the tangent to the curve is horizontal. (b) State whether each such point is a local maximum, minimum or point of inflection.

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