Problem #3: Consider the following function. f(x, y) = x3+18xy-912 (a) Find the critical points of f. (b) For each critical point in (a), find the value of det[H(xo, yo)] from the Second Derivative test that is used to classify the critical point. Separate your answers with a comma. Your first value of det[H(xo, yo)] must correspond to the first critical point in (a) [i.e., the critical point (0, 0)], and your second value of det! H(xo, yo)] must correspond with the second critical point. (c) Use the Second Derivative test to classify each critical point from (a). Note that for each given answer, the first classification corresponds to the first critical point in (a) [i.e., the critical point (0,0)] and the second classification corresponds to the second critical point in (a). (A) (0, 0), (6,6) (B) (0,0), (6,-6) (C) (0, 0), (-12, -12) (D) (0, 0), (12, 12) (E) (0, 0), (12,-12) (F) (0, 0), (-6,-6) (G) (0, 0), (-6,6) (H) (0,0), (-12, 12)

The point Q (-4,7) lies on the function f(x). Suppose f(x) is transformed according to: y=-3 f [0.5(x + 3)] + 5. Determine the x-coordinate of the transformed point, Q'. Enter only the x-coordinate, a single value, rounded correctly to 2 decimal places (ie 3.46 or 7.00 or 1.50)

1) Consider f(x) = 3x4 -8x³ +6 a) Find all critical points of the function (make sure to consider if the derivative is defined everywhere or not!). Label them in increasing order, 21, 22, 23, etc (for how many you find). b) Use the first derivative test to determine if x₁ is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y). 1 c) Use the second derivative test to determine if x2 is a local max, min, or neither. Find the y value associated with this a value and write it as a point (x, y).