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I'm struggling with this question. Could you please help me with
the correct answers and show me the steps.
Question) A hiker on the surface H x, y = 14 − 4𝑥 2 − 3𝑦 2 is
standing at the point (1, −1, 7). All distances x, y and z are in
kilometers. The positive 𝑥 − 𝑎𝑥𝑖𝑠 points east and the positive 𝑦 −
𝑎𝑥𝑖𝑠 points north.
a) Find the directional derivative at 𝑥_0 = 1 and 𝑦_0 = −1, when
facing toward the point (2, 3). That is, find the directional
derivative from point 𝑃(1, −1) to point 𝑄(2, 3).
b) If the hiker walks in a Southeast direction will she start to
ascend or descend? At what rate?
c) From where the hiker is standing, in which direction is the
steepest ascent on the surface?
d) What is the maximum rate of ascent in that direction?
e) What are the units for the directional derivative in part
(d)
Thank you,will rate