4.4 4.7

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4.4

4 4 4 7 1 (23.17 KiB) Viewed 27 times

4 4 4 7 2 (18.01 KiB) Viewed 27 times

4.7

4 4 4 7 3 (13.86 KiB) Viewed 27 times

An engineer is building experimental, dome-shaped living quarters 304 m high and modeled by the function z=304−4x2−8y2. She wants to bolt a flat solar panel to the dome at the point (5,5,4). Find the vector of the direction in which the engineer should drill. (Give your answer using component form or standard basis vectors. Express numbers in exact form. Use symbolic notation and fractions where needed.) directiol
Determine the point(s) on the surface z=24x−12y−4x2−3y2 at which the tangent plane is parallel to the xy-plane. (Give your answer as a comma-separated list of coordinate points of the form (∗,∗,∗). Express numbers in exact form. Use symbolic notation and fractions where needed.)
(x,y,z)=(3,−2,−1) Incorrect
Incorrect
Find the absolute maximum and absolute minimum of the function z=f(x,y)=14x2−56x+14y2−56y on the domain D:x2+y2≤81 (Use symbolic notation and fractions where needed.) absolute min: absolute max:
Find the local maxima, local minima, and saddle points, if any, for the function z=15x+5yx​ (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (∗,∗,∗),(∗,∗,∗)… Enter DNE if the point does not exist.) local min
Find the local maxima, local minima, and saddle points, if any, for the function z=3x3−36xy−3y3. (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (∗,∗,∗),(∗,∗,∗)… Enter DNE if the points do not exist.) local mir local max: saddle poin
Find the local maxima, local minima, and saddle points, if any, for the function z=4x3−60xy+4y3. (Use symbolic notation and fractions where needed. Give your answer as point coordinates in the form (∗,∗,∗),(∗,∗,∗)… Enter DNE if the points do not exist.) local min: local max: saddle points: