The question is in the attachment and my work is also in the attachment.
My reasoning:
I labelled the points on the graph. Let z be the contour map function
1) At the point (0,2) if you go up, z changes from 4 to 6 so the directional derivative is positive
2) At the point (0,-2), in the direction of the vector <1,-2>, z becomes more positive so directional derivative is positive
3) At the point (1,0), z changes from 0 to positive so directional derivative is positive
4) At the point (-1,1) z moves parallel to the contour so the directional derivative is zero
5) At point (-2,2), z moves right, from 8 to 6 so directional derivative is negative
6) At point (-1,1), z moves towards the top left hand side so z becomes more positive and the directional derivative is positive.
But apparently one or more of the parts are wrong. Which one is it? I've checked over my reasoning and I can't find my error.
My reasoning:
I labelled the points on the graph. Let z be the contour map function
1) At the point (0,2) if you go up, z changes from 4 to 6 so the directional derivative is positive
2) At the point (0,-2), in the direction of the vector <1,-2>, z becomes more positive so directional derivative is positive
3) At the point (1,0), z changes from 0 to positive so directional derivative is positive
4) At the point (-1,1) z moves parallel to the contour so the directional derivative is zero
5) At point (-2,2), z moves right, from 8 to 6 so directional derivative is negative
6) At point (-1,1), z moves towards the top left hand side so z becomes more positive and the directional derivative is positive.
But apparently one or more of the parts are wrong. Which one is it? I've checked over my reasoning and I can't find my error.
