Suppose that f(x, y) is a smooth function and that its partial derivatives have the values, fx(−6,7)=−1 and fy(−6,7)=4. Given that f(−6,7)=4, use this information to estimate the value of f(−5,8). 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.

It is saturday morning and jeremy has discovered he has a leak coming from the water heater in his attic. since plumbers charge extra to come out on the weekends, jeremy is planning to use buckets to catch the dripping water. he places a bucket under the drip and steps outside to walk the dog. in half an hour the bucket is 1/5 of the way full. what is the rate at which the water is leaking per hour?