Consider f(x,y,z)=1+sin(x+2y-z); P(π6, π6, -π6); u⇀={“versio…

Consider f(x,y,z)=1+sin(x+2y-z); P(π6, π6, -π6); u⇀={“version”:”1.1″,”math”:”f(x,y,z)=1+sin(x+2y-z); P(π6, π6, -π6); u⇀=<1,2,2>”}. (a) Compute the gradient of f{“version”:”1.1″,”math”:”f”} and evaluate it at P. (b) Find the directional derivative at P in the direction of u⇀{“version”:”1.1″,”math”:”u⇀”}. (You do not need to type your answers in the space below. However, you must upload a file of your handwritten work in the final question.

Consider the following function and the given region f(x,y)=…

Consider the following function and the given region f(x,y)=2×2+y2; R={(x,y): x2+y2≤16}{“version”:”1.1″,”math”:”f(x,y)=2×2+y2; R={(x,y): x2+y2≤16}”}. Find the absolute maximum and minimum values using the method discussed in 15.7. (You do not need to type your answers in the space below. However, you must upload a file of your handwritten work in the final question.)