Question

A particle moves along the x-axis so that its position at any time t> 0 is given by x(t) = t^4 - 10t^3 + 29t^2 - 36t +2. For which value of t is the speed the greatest?

Answer 1

Speed is the derivative of distance, x(t), with respect to time.
                        speed = dx/dt = 4t³ - 30t² + 58t - 36
The time at which the speed is greatest is the derivative of the speed equated to zero.
                     ds/dt = 12t² - 60t + 58 = 0
The value of t from the equation are 3.69 and 1.31 seconds.