{Use of Tech} Bungee jumpe​​r A woman attached to a bungee cord jumps from a bridge that is 30 m above a river. Her height in meters above the river t seconds after the jump is y(t) = 15(1+e^−t cos t), for t ≥ 0.
b. Use a graphing utility to determine when she is moving downward and when she is moving upward during the first 10 s.  

Verified step by step guidance

1. First, identify the function that represents the height of the woman above the river: y(t) = 15(1 + e^{-t} ext{cos}(t)).
2. Next, find the derivative of the height function y(t) with respect to time t, which will give you the velocity function v(t). This is done using the product rule and chain rule of differentiation.
3. Set the velocity function v(t) equal to zero to find the critical points, which will indicate when the woman changes direction (from moving upward to downward or vice versa).
4. Evaluate the sign of the velocity function v(t) in the intervals determined by the critical points to determine when she is moving upward (v(t) > 0) and when she is moving downward (v(t) < 0).
5. Use a graphing utility to visualize the height function y(t) and the velocity function v(t) over the interval from t = 0 to t = 10 seconds to confirm your findings.