What is the directional derivative of the mountain at point P towards the peak?

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SUMMARY

The discussion focuses on calculating the directional derivative of a mountain represented by the equation h(x,y) = 400 - (1/10000)x² - (1/2500)y² at a specific point P, located 1600 meters West and 400 meters South of the peak. The peak is identified as the point (0,0). The user initially struggled to find the correct directional vector towards the peak but ultimately resolved the issue by correctly calculating the gradient without including the incorrect terms. The final answer for the slope in the direction of the peak is 8/5√17.

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Homework Statement


A bush-walker is climbing a mountain, of which the equation is h \left( x,y \right) =400-{\frac {1}{10000}}\,{x}^{2}-{\frac {1}{2500}<br /> }\,{y}^{2}<br />

The x-axis points East, and the y-axis points North. The bush-walker is at a point P, 1600 metres West, and 400 metres South of the peak.

What is the slope of the mountain at P in the direction of the peak?

The Attempt at a Solution



I'm fairly sure on how to solve this, except I need a few different elements. Since we have the starting point, I can calculate the gradient at that point. I need to find a directional vector (to the peak) from that point, and that's what I'm not sure to find.

Looking at the equation for the mountain, I'm guessing its peak is when (x,y) = (0,0)

I first tried for v = +1600i + 400j, but that was not correct.

The answer 8/5*sqrt(17) = 0.388
 
Last edited:
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NVM, I figured it out. I was mistakenly keeping the 400 as part of the equation whilst calculating the gradient.
 
Last edited:

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