Originally Posted by

**billym** I have this function again:

$\displaystyle

f(x,y) = x^4 + 2x^2y^2 + y^4 + 2x^2 - 2y^2 + 6

$

The value of $\displaystyle f$ when $\displaystyle x = -1$ and $\displaystyle y = 2$ is $\displaystyle 25$.

The maximum percentage error in the value of $\displaystyle x$ is $\displaystyle 2 $% and the maximum percentage error in the value of $\displaystyle y$ is $\displaystyle 3$%.

I have to find the least and greatest possible values that $\displaystyle f(-1,2)$ can take, and the maximum possible percentage error in taking the value $\displaystyle f(-1,2) = 25$.

I plugged $\displaystyle -1$ and $\displaystyle 2$ into the partial derivatives:

$\displaystyle

f$x$\displaystyle (-1,2) = 4(-1)[(-1)^2 + (2)^2 + 1] = -24

$

$\displaystyle

f$y$\displaystyle (-1,2) = 4(2)[(2)^2 + (-1)^2 - 1] = 32

$

And then found:

$\displaystyle

\delta f = -24(0.02)(-1) + 32(0.03)(2) = 2.4

$

So the least and greatest possible values for $\displaystyle f(-1,2)$ are $\displaystyle 22.6$ and $\displaystyle 27.4$, and the maximum possible percentage error is $\displaystyle 9.6$% ?

Is there anything correct here or am I completely wrong?