Question

Please answer all the questions (and in a neat format). Thanks!

(see photo)

Need all the answers at a glance.

Answer 1

#15

For \(f_x\) we keep \(y\) fixed and see how the function changes as we change \(x\)

so simply look at rows

Answer 2

yes! we have to apply this formula:
\[\Large {f_x}\left( {{x_0},{y_0}} \right) \cong \frac{{f\left( {{x_0} + \Delta x,{y_0}} \right) - f\left( {{x_0},{y_0}} \right)}}{{\Delta x}}\]

Answer 3

In each row, as \(x\) is increasing, notice that the function is decreasing.


In light of that, what can you say about the sign of \(f_x\) ?

Answer 4

The sign is positive, but decreasing....?

Answer 5

nope, remember how first derivative can be used to tell whether a function is increasing/decreasing from single variable calculus ?

Answer 6

Somewhat, yes, but muddy.

Answer 7

First derivative at a particular point on the curve gives the slope of tangent line at that point

Answer 8

Notice that the slope of tangent line will be "positive" in the interval in which the function is "increasing"