Let (x,y)= (5y) / (4 + e^(2xy^2)). Find the maximum rate of change of f at the point (0, 3) and the direction in which it occurs.

Question

Let (x,y)= (5y) / (4 + e^(2xy^2))

Find the maximum rate of change of f at the point (0, 3) and the direction in which it occurs.

Answer 1

Hi James N.,

You can actually reason this one out without hauling out the calculus. Why not?

Since x=0 at this point, the whole exponential expression in the denominator is exp(0) = 1. You can't make that negative, so as to decrease the denominator, so leave it alone == don't change the x, change the y only!

So that should be a pretty easy choice, boosting the value by raising y. Just move in a positive y direction. If you wanted it to decrease maximally, slide it downwards.

--Cheers, --Mr. d.