Calculus  Still Need Help! Anyone!
posted by Leanna .
A particle moves along the xaxis 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.

a. Find the derivative, set to zero
dx/dt= e^t * sint+ e^tcost=0
tanT=1 check that.
t= PI/4 or 3PI/4
Now which will make it to the left (negative x)?
b. d^2x/dt^2= d/dx e^t(costsint)
take that dervative.
Then, put in the equation given
ax" + x'+ x=0 and solve for A