QUESTION 9 16 p Let f(x)=x4e-* (a) Find the critical points of f(x). (b) Find the...
(10 points) Find the critical numbers of the function f(x) = (x - 3) 323/2 (15 points) Find the absolute maximum and absolute minimum values of f(x) = interval (0,3) 2-1+1 on the
Cal 4
, ) and use this to 6. Let f(x,y) = x2 + y2 + 2x + y. (a) Find all critical points of f in the disk {(x,y) : x2 + y2 < 4). Use the second derivative test to determine if these points correspond to a local maximum, local minimum, or saddle point. (b) Use Lagrange multipliers to find the absolute maximum/minimum values of f(x, y) on the circle a2 +y -4, as well as the points...
Apps 3. G Gmail YouTube Maps -11 POINTS SCALCET8 4.1.029. Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) F(x) = 9 + 1x - * Submit Answer -/1 POINTS SCALCET8 4.1.030. Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) P(X) = x++ 3x2 - 105X - /2 POINTS SCALCET8 4.1.048. Find the...
5.1 (10 points): Let f(x,y) = 4 – 22 – y? Find all extrema (both relative and absolute) on the square D = {(x, y): 0 535 2,0 Sy <2}. 5.2 (10 points): Let f(x,y) = ry–2x+3y+100. Classify all critical points (rela- tive minimum, relative maximum, saddle point), and find the absolute maximum and absolute minimum on the triangle enclosed by the lines x = -4, y = 4, and y=++3.
7. [23] Given the following function:: f(x)-x-4x +6 (a) Find all of the critical points of this function. Show your work. (b) Characterize each of the critical points as a local maximum, a local minimum or neither. Show your work. (c) Find all of the inflection points of this function (verify that it/they are indeed inflection points). (d) On what interval(s) is this function both decreasing and concave down? on the interval -15xs1. Show (e)Find the global maximum and minimum...
(5 points) Let f(x) = 5x2e-3x (a) Find all critical numbers of f. (b) Find the x-coordinates of the inflection points on the graph of f. (c) Fill out the chart below and roughly sketch the graph of y = xée 2* Interval Test value x Sign of f'(x) Sign of F"(x) Concavity Rough Graph
Let f(x)=x^3−(3/2)x^2 on the interval [−1,2]. Find the absolute maximum and absolute minimum of f(x) on this interval. The absolute max occurs at x= . The absolute min occurs at
Let ?(?)=?2−8?+4f(x)=x2−8x+4.
(1 point) Let f(x) = x2 – 8x + 4. Find the critical point c of f(x) and compute f(c). The critical point c is = The value of f(c) = Compute the value of f(x) at the endpoints of the interval [0, 8]. f(0) = f(8) = Determine the min and max Minimum value = Maximum value = Find the extreme values of f(x) on [0, 1]. Minimum value = Maximum value =
QUESTION 7 Find all the critical points for f(x,y)=-x® + 3x - xy and classify each as a local maximum, local minimum or a saddle point. (9 marks)
1. Suppose that f(x) has a critical number at x=c, and f′′(c)=−10 By the Second Derivative Test, we conclude A. the test is inconclusive. B. x=c is an inflection point C. x=c is a local (relative) minimum D. x=c is a local (relative) maximum E. x=c is an absolute minimum Question 4 of 10 3 Points What follows is a numeric fill in the blank question with 2 blanks. Find the absolute maximum and minimum value of the function f(x)=0.5x^4+(4/3)x^3−3x^2+4...