# Math Help - estimates based on partial derivatives

1. ## estimates based on partial derivatives

hello
ive got a quiz tomorrow, and this is one of the example questions
i have looked through my text and my notes, and havent found anything that could help me.

Suppose that is a smooth function and that its partial derivatives have the values, and . Given that , use this information to estimate the following values:

Estimate of (integer value)
Estimate of (integer value)
Estimate of (integer value)

at first I was trying to come up with a function that would satisfy that derivatives and the function, but it turned out to be harder than i thought. what do i need to do?

2. Use linear approximation: $f(0,-7) = f(0,-8+1) \approx f(0,-8) + 1\cdot f_y(0,-8)$
Now substitute the numerical values.
Do the same thing with other ones.

3. ah thank you!