A curve has the equation y=e2xy = e^{2x}y=e2x
Find, in terms of aaa, the equation of the tangent to the curve at the point (a,e2a)(a, e^{2a})(a,e2a)
Find the value of a a\,a for which this tangent passes through the origin.
Hence, find the set of values of m m\,m for which the equation e2x=mxe^{2x} = mxe2x=mx has no real solutions.
Practise Edexcel AS Level Maths Exponentials and Logarithms with exam-style questions for AS Level Maths. 41 questions covering 14.1 Exponential Functions, 14.2 y = e^x, 14.3 Exponential Modelling, 14.4 Logarithms, 14.5 Laws of Logarithms, 14.6 Solving Equations using Logarithms, 14.7 Working with Natural Logarithms, and 14.8 Logarithms and Non-Linear Data, matched to the Edexcel AS Level Maths (8MA0) specification and written in Paper 1 and Paper 2 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.