Suppose that f(x,y,z) is a smooth function such that f(p)=0 where p=(1.4420, -2.

Question

Suppose that f(x,y,z) is a smooth function such that f(p)=0 where p=(1.4420, -2.8118, -1.73200) and suppose that z(x,y) satisfies f(x,y,z)=0 and p is on the graph of z(x,y). Estimate the percent change in z (new minus old divided by old times 100) when x is increased by 9 percent of its value in p and y is decreased by 5 percent of its value in p, given the rates of changes of f at p along the vectors a, b, and c are :

where a, b, and c is an orthomormal basis with

a=(-0.993205, 0.029644, -0.112542), b=(0.115404, 0.375896, -0.919448), c=(0.015048, -0.926188, -0.376762).

Suppose that f(x,y,z) is a smooth function such that f(p)=0 where p=(1.4420, -2.8118, -1.73200) and suppose that z(x,y) satisfies f(x,y,z)=0 and p is on the graph of z(x,y). Estimate the percent change in z (new minus old divided by old times 100) when x is increased by 9 percent of its value in p and y is decreased by 5 percent of its value in p, given the rates of changes of f at p along the vectors a, b, and c are : where a, b, and c is an orthomormal basis with a=(-0.993205, 0.029644, -0.112542), b=(0.115404, 0.375896, -0.919448), c=(0.015048, -0.926188, -0.376762).

Explanation / Answer

5.78

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