A Level Maths exam question on functions - differentiation and graph transformations

This A level exam question explores the graph of a function, and involves differentiation with exponentials, the product rule, finding stationary points, graph transformations, and the range of functions. Lots of skills to practice!
Enjoy!
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[@StarfishMaths]

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[@StarfishMaths]

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[@johnpro2847]

would you get 14 mins to answer i question?

[@johnpro2847]

that is not easy..