Suppose that f(x,y) is a smooth function and that its partial derivatives have the values, fx(4,−7)=−3 and fy(4,−7)=1. Given that f(4,−7)=−8, use this information to estimate the value of f(5,−6). Note this is analogous to finding the tangent line approximation to a function of one variable. In fancy terms, it is the first Taylor approximation.
a) Estimate of (integer value) f(4,−6)
b) Estimate of (integer value) f(5,−7)
c) Estimate of (integer value) f(5,−6)

Question

Suppose that f(x,y) is a smooth function and that its partial derivatives have the values, fx(4,−7)=−3 and fy(4,−7)=1. Given that f(4,−7)=−8, use this information to estimate the value of f(5,−6). Note this is analogous to finding the tangent line approximation to a function of one variable. In fancy terms, it is the first Taylor approximation.
a) Estimate of (integer value) f(4,−6)
b) Estimate of (integer value) f(5,−7)
c) Estimate of (integer value) f(5,−6)