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 AQA A Level Maths 1.9 F: Exponentials and logarithms with exam-style questions for A Level Maths. 37 questions covering 1.9.1 Exponential functions and their graphs, 1.9.2 Gradient of e^kx (A-level only), 1.9.3 Logarithms as inverse functions, 1.9.4 Laws of logarithms, 1.9.5 Solving exponential equations, 1.9.6 Logarithmic graphs to estimate parameters (A-level only), and 1.9.7 Exponential growth and decay, matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 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.
