MATH 205 Midterm: MATH 205 KSU Test 3f04

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turquoisegnu128

15 Feb 2019

School

Kansas State University

Department

Mathematics

Course

MATH 205

Professor

All

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Document Summary

For full credit, show your work in detail. Total: 100 #1 #2 #3 #4 #5 #6 #7 #8. Find all in ection points of the function f (x) = x4 + x3 3x2 + 2. Let f (x) = 3 ln x x: (a. Find x at which f (x) has a critical point, determine if it is a local minimum, local maximum or neither: (b. Find the global minimum and maximum of above f (x) over the interval. The number p of customers will purchase a certain new product by tth day since it has come to the market is given by the logistic model: page 2. How many customers purchase this product as soon as it is available : (5 pts). Approximatlt how long will it take until it reaches the point of diminishing return ? (show your work): 15pts. The average cost function of a product is a(q) = 0. 01q2 0. 6q + 13: (a 5pts. )

Related Questions

Please answer numbers 2c, 3a, and 3b. Please and thank you.

1. (45 marks) Short-Answer Questions. Put your answer in the box provided but show your work also. Each question is worth 3 marks, but not all questions are of equal difficulty. Full marks will be given for correct answers placed in the box, but at most 1 mark will be given for incorrect answer. Unless otherwise stated, it is not necessary to simplify your answers in this question. a) Find the equation of the tangent plane to the graph of the function z = f(x,y) = sell at (0,1). Answer b) Evaluate (T, 0) if f(x,y) = sin(ry). Answer c) Graph of a function z = f(x,y) is given by: Which of the following level curves correspondes to this function. Answer d) If f(x,y) = e(3x – 2y), find lim - Math)-f(x,y) e) Find % if f(x, y) = x2 - y3 and 2 = r sin(t), y = r cos(t). Answer f) Evaluate the directional derivative of f(x, y) = !at (1, -1) in the direction of u =(2, 1). Answer 8) Does Simono converge? h) Sketch the direction field of the differential equation = 1-2y. i) Consider the differential equation ay = 15 - 31, y(0) = 0, and use Euler's method with step size 0.1 to estimate y(0.1). Answer j) Knowing that (-3,-3) is a critical point of f(x,y) = 2:3 + y2 – 4.cy -3.0, use the second derivative test to find out whether it is a local minimum, local maximum, or a saddle point. Answer k) Solve the initial value problem, dy dt 642 2y + cos(u) y(1) = . Answer 1) Is ū=(2,2, -1) perpendicular to v = (5,-4, 2)? Answer m) Find the area between the graph of y = 1 + sin(x) and y=1-sin(x) from 0 to 7. Answer n) Determine the lentgh of the curve y = 8/2,0 SIS 3. Evaluate and simplify your answer. Answer o) Express the volume of the solid obtained by rotating the bounded region that lies between curves y = (x-2)2 and y=1,150 $4 about the vertical line 2 = 5. Do not evaluate this integral. Answer

MATH 205 Midterm: MATH 205 KSU Test 3f04

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