By Lagrange’s multiplier method, we can find __________________.

If the limits of an integral involves the variables of integration then the order of integration depends by the order the terms dx, dy and dz are written.

\lim_{x \to 1} \lim_{y \to 1} \frac{x(y-1)}{y(x-1)}

If  u = x^2 - y^2 and v = 2xy  then   \frac{\partial(u,v)}{\partial(x,y)} is _______________.

Rolle's theorem is a direct consequence of the Mean Value theorem.

Concavity of a function changes at critical points.

We can test the continuity of a function at the point (1,2) along the curve y = x.

The function f(x) = x^{2/3}, \quad x \in [-1, 8] satisfies the hypotheses of the Mean Value Theorem.

If f′ changes from negative to positive at c, then f has a local maximum at c.

Find the value or values of c that satisfy the equation in the Mean Value Theorem for the function f(x) = x^2 + 2x - 1, \quad x \in [0, 1]