A differentiable function models the height (in meters) of a drone above the ground…
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A differentiable function h models the height (in meters) of a drone above the ground as a function of horizontal distance x (in meters) traveled from its launch point on a straight flight path. Engineers recorded the following information from the screen of their flight-analysis software.
Graphical observations (verbal description):
(a) Identify the x-coordinate(s) of all critical points of h on the interval 0≤x≤60, and explain why each point is a critical point.
(b) Using only the features described above, determine the open intervals on which h is increasing and on which it is decreasing. Justify your answer.
(c) Classify each critical point you identified in part (a) as a local maximum, local minimum, or neither. Provide a justification that references changes in the sign of h′(x) or concavity, as appropriate.
(d) Explain the practical meaning, in the context of the flight, of the local extremum that occurs at x≈20. Include units in your response.