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Exam-Style Question on CalculusA mathematics exam-style question with a worked solution that can be revealed gradually |
Question id: 569. This question is similar to one that appeared on an IB AA Standard paper in 2021. The use of a calculator is allowed.
Consider the function \(f\) defined by \(f(x) = 25e^{x-5}\) for \(x \in \mathbb{R}^+\).
(a) Find the coordinates of the points where the graph of \(f\) intersects the line \(y=x\).
The line \(L\) has a gradient of \(-1\) and is a normal to the graph of \(f\) at the point \(R\).
(b) Find the exact coordinates of \(R\).
(c) Show that the equation of the line \(L\) is \(y=-x+6- \ln{25}\).
(d) Find the area of the region enclosed by the graph of \(f\) and its inverse.
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