Find the x co-ordinates of the stationary points of the graph with equation y = cos(x)7e^(x). Give your answer in the form x = a +/- bn where a/b are numbers to be found, and n is the set of integers.

The stationary points on a curve of the form y=f(x) are where dy/dx = 0. To find dy/dx, differentiate using the product rule: dy/dx = 7e^x(d/dx(cosx)) + cosx(d/dx(7e^x)) = -sinx(7e^x) + cosx(7e^x). Now set dy/dx = 0: -sinx(7e^x) + cosx(7e^x) = 0. Factorising and dividing both sides by 7 gives: e^x(cosx - sinx) = 0. e^x never equals zero, hence we have cosx - sinx = 0. Taking sinx to the other side and dividing both sides by cosx gives: tanx = 1. We have x = arctan(1) = pi/4 using a calculator. Since tanx is repeats every pi radians, the complete range of solutions is x = pi/4 +/- npi where n is the set of integers.