The horizontal position of an object from a point of origin in meters is modeled by the function x(t)= (1+sin(t))/(2+cos(t)) where t is measured in minutes and 0 is less than or equal to t which is less than or equal to 5.
A) show that x(t)= (2cos(t)+sin (t)+1)/(2+cos(t))^2
B) find the velocity when t=pie
C) it is known that the graph of t is concave down at t=pie determine if the object is speeding up or slowing down when t=pie.
I believe for A it is just derivative of base equation. I believe for B I need to plug pie into the derivative C I believe is just a rule if first and second derivate have same sign its accelerating if its opposite then its decelerating. Im looking for second opinion if this is right way to do it. Thanks
A. No, x(t)=x(t), no derivatives. In fact, they are not equal: consider t=0, the first x(t)=1/2, and the second x(t)=3/3. Somehow, something is wrong.
B. velocity= x'(t) at t=PI
C. find second derivative, acceleration is negative, slowing down.