For each of the following statements, determine whether the statement is true or false. In each case, explain why your determination is correct.
If $f (x,y)$ is a continuous function and $∇f (a,b) = 5$, then there is no direction from the point $(a,b)$ for which the derivative equals $-7$.
A function $f(x,y)$ can have two local maxima and no local minima.
If two surfaces are tangent to one another, their normal lines at the point of tangency are Perpendicular to each other.
We can always change the order of integration in double integrals.
Please Correct me, 1) false 2) true 3)false (they should be parallel 4) true