Question

A particle moves along the x-axis with position at time t given by x(t)=e^(-t)sin(t) for 0 is less than or equal to t which is less than or equal to 2 pi.

a) Find the time t at which the particle is farthest to the left. Justify your answer

I think you have to find the prime of this equation and then see when it is negative.

b) Find the value of the constant A for which x(t) satisfies the equation Ax"(t)+x'(t)+x(t)=0 for 0 is less than t which is less than 2 pi.

I have no idea how to even start this problem.