d= √500t^2 -240t -29
(b) Use a graphing utility to graph d=d(t). For what value of t is d smallest?
t≈ hours
To find the value of t that corresponds to the smallest value of d, we can first graph the function d(t) = √(500t^2 - 240t - 29) using a graphing utility.
After graphing the function, we can visually identify the point on the graph where the function reaches its minimum value of d. This point represents the value of t where d is smallest.
Alternatively, we can use calculus to find the exact value of t where d is smallest. By taking the derivative of the function d(t) with respect to t, setting it equal to zero, and solving for t, we can find the critical points which correspond to the minimum value of d.
Once we have the value of t where d is smallest, we can approximate it to find the value in hours.