Questions from General Calculus

Q: Suppose (1, 1) is a critical point of a

Suppose (1, 1) is a critical point of a function f with continuous second derivatives. In each case, what can you say about f?

Q: Find the local maximum and minimum values and saddle point(s

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the impor...

Q: Find the equation of the tangent plane to the hyperboloid x2/

Find the equation of the tangent plane to the hyperboloid x2/a2 + y2/b2 - z2/c2 = 1 at (x0, y0, z0 ) and express it in a form similar to the one in Exercise 51. Exercise: Show that the equation of t...

Q: Use a tree diagram to write out the Chain Rule for the

Use a tree diagram to write out the Chain Rule for the given case. Assume all functions are differentiable. u = f (x, y), where x = x (r, s, t), y = y (r, s, t).

Q: / (a). Find the gradient of f.

(a). Find the gradient of f. (b). Evaluate the gradient at the point P. (c). Find the rate of change of f at P in the direction of the vector u.

Q: Use the Chain Rule to find dz/dt or dw/

Use the Chain Rule to find dz/dt or dw/dt. z = xy3 - x2y, x = t2 + 1, y = t2 - 1

Q: Suppose (0, 2) is a critical point of a

Suppose (0, 2) is a critical point of a function t with continuous second derivatives. In each case, what can you say about t?

Q: A table of values for the wind-chill index W =

A table of values for the wind-chill index W = f (T, v) is given in Exercise 14.3.3 on page 923. Use the table to estimate the value of Du f (-20, 30), where u = (i + j)/ 2 . Table from Exercise 14.3...

Q: Find the local maximum and minimum values and saddle point(s

Find the local maximum and minimum values and saddle point(s) of the function. If you have three-dimensional graphing software, graph the function with a domain and viewpoint that reveal all the impor...

Q: / (a). Find the gradient of f .

(a). Find the gradient of f . (b). Evaluate the gradient at the point P. (c). Find the rate of change of f at P in the direction of the vector u.