Question

(10 pts) Let g(x) = x - Ve (a) List the steps of the closed interval method. (b) Find the absolute maximum and absolute minimum values of the function g(x) on (0,4), and indicate where it is achieved. (15 points) Let p(t) be a position function, and v(t), a(t) be the associated velocity and acceleration functions. (a) Using only the above functions and the symbol , describe the relationship be- tween position and velocity and between velocity and acceleration. (b) If a(t) = -10 and v(0) = 5, find an expression for v(t). (C) If y(t) is as above, and p(1) = 1, find an expression for p(t)

Answer 1

The solution is given below

g(x) = x-&x at x=4, 9149 = 4-V4 Stop Güven, function on (0,47 step: firstly we find the end point function value at x=0, gio) = 0 964) = 2 step®: Now, we find the critical point of the giun function, g'(x) = CR-VW) => delta (x -x2) 1- 1 x 2 - 1 1 - 1 x 2 grw = 3x12 Now, we find the function value at critical point- da = 0 » xk+ > x=1 2. 2-1 4 we have' > g) - -l I 4 2 11 g(t) = - .L 4 step : 9641=2 is the largest function value ceo, g141 = 2 is global maximum value. It is the smallest function value. iile, 944) = 3 in the global minimum value. and g(4) =