I believe I figured out a and b. For a) any vector perpendicular to the gradient at (1,1). This is <-1/8, 1/4> and <1/8,-1/4> divide by magnitude of each vector. For b) it will be the gradient at (1,1) as a unit vector, then dot this with the gradient at (1,1) to get slope. For c) I set up 0.25=<-1/8,-1/4> dot <a,b>, but I'm not sure how to get the exact solutions for a and b. For d) Should I take the gradient of r(x,y) at t = 0?

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3. You are hiking up a mountain whose elevation {in ho) is 1 f{1=1y)= m when you are 3: km east and 3; km north of the peak. You are currently resting at position (I, y) = (1, 1), deciding how to proceed. (a) In which direction(s) should you move to maintain your current elevation? {13) In which direction{s) is the ascent steepest? 1What is the grade (slope, expressed as a percentage) in that direction? (c) You think you can handle a 25% grade ascent. Which direction{s) achieve that? (d) If you set off along a path described by :I:{t) = 2—25, y(t) = 1 — t (t in hours), at what (initial) rate is your elevation increasing?

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