Find all the critical points of the function f(x) = x2 - 6x + 13. Explain...
Find the linearization of the function f(x) = 5 + x2 at x = 2. Explain how you arrive at your answer.
(a) Find and classify all of the critical points of the function X f(x, y, z) = (x2 +42 + x2)3/2 on the unit sphere. (b) Find and classify all of the critical points of the function f(x, y, z) = x sin(x2 + y2 +22) on the sphere of radius
5. Let f(x,y) = 3x2 y - y3 - 6x. (a) Find all the critical points off. (b) Classify each of the critical points; that is, what type are they? (c) For the same function f(x,y), find the maximum value of f on the unit square, 0 SX S1,0 <y s 1.
7. Find all critical points of the following function. f(x) = 5x3 – x2 – 3x +2 a) x = -1,3 b) x = 2,3 c) x= -2,2 d) None of the above
4. Given the function f(x,y) = 4+x2 + y3 – 3xy. a. Find all critical points of the function. b. Use the second partials test to find any relative extrema or saddle points.
Let f(x) = x2 - 5 and g(x) = 6x + 1. Find the function. fog (f.g)(x) = Find its domain. (Enter your answer using interval notation.)
#3 please!!
2. Given the function f(x, y)-x2 +y -2xy -6x - 2y 5, find the following: (a) Find the critical point(s) of the function. For full credit, show all the algebra to find these and give your answer as ordered pairs. (b) Find the second order partial derivatives and use these to find the determinant of each critical point. Then classify each critical point as a saddle point, relative minimum, or relative maximum point. 3. A wine dealer sells...
(1 point) Consider the function f(x, y) = e-8x=x2-4y—y2 Find and classify all critical points of the function. If there are more blanks than critical points, leave the remaining entries blank. fx = fxx = fxy =
8) Find the average rate of change for the function f(x) = -x2 + 6x on the interval [3,5).
3. Consider the function f(x) = x2 - 6x^2 - 5 a. Find the values of x such that f'(x) = 0. b. Use the results of part a to: find interval(s) on which the function is increasing and interval(s) on which it is decreasing. c. Find the value(s) of x such that f"(x)=0. d. Use the result of part c to find interval(s) on which f(x) is concave up and interval(s) on which it is concave down. e. Sketch...