2024 IGCSE Additional Mathematics May/June 0606/22 Q5

6 marks

A curve has equation \(y=5\mathrm{e}^{2x-1}+\mathrm e\). The tangent to the curve at the point where \(x=1\) cuts the \(x\)-axis at the point \(P\).

Find the equation of the tangent in the form \(y=mx+c\), where \(m\) and \(c\) are exact values, and hence find the \(x\)-coordinate of \(P\).[6]

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Answer:\(y=10\mathrm e x-4\mathrm e\); \(x\)-coordinate of \(P=\dfrac25\).

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