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# Calculus for Business MTH 203

Marshall

GPA 3.51

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This 0 page Study Guide was uploaded by Pansy Cronin on Sunday November 1, 2015. The Study Guide belongs to MTH 203 at Marshall University taught by Staff in Fall. Since its upload, it has received 51 views. For similar materials see /class/233248/mth-203-marshall-university in Mathematics (M) at Marshall University.

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Date Created: 11/01/15

STUDY SHEET for TEST 2 Monday November 7 The test will cover Ch 9 Section 98 Ch 10 Sections 101 102 103 104 105 Ch 11 Section 11 The best way to prepare to the midterm is to read the book and to do the homework exercises Please take time to go over the material Here is what you have to have an idea about 1 Marginal functions in economics 98 2 Increasing and decreasing functions 101 3 Determining the intervals where a function is increasing or decreasing 101 4 Finding the relative extrema Critical points The first derivative test 101 5 Determining the interval of concavity In ection points 102 6 Curve sketching for polynomial and rational functions Vertical and horizontal asymptotes 103 7 Optimization Absolute extrema Finding absolute extrema of a function on a closed interval 104 8 Solving optimization problems Maximization problems minimization problems inventory problems 105 9 Antiderivatives The indefinite Integral 111 10 Basic integration rules 111 11 Differential equations Initial value problem 111 Below is the list of typical problems in the most general from which you can expect on the test 1 Given the cost or revenue or profit function find the actual cost revenue profit for manufacturing and additional unit of commodity See exercises 3 on page 691 2 Marginal Cost Marginal Average Cost Marginal Revenue and Marginal Pro t See exercises 5 9 11 and 13 on page 691 3 Find the intervals where each function is increasing and the intervals where it is decreasing a fx5x 7 b fx2x2x1 c fx x2 x 1 4 Given the graph of a function determine the relative maxima and relative minima if any See exercises 4148 on page 712 5 Find the relative maxima and relative minima if any of the given function a fxx3 3x6 c fx 2x1 x b fx2x23x7 d fxxze gt1 9 0 N LA NNNl D ID I Nt IOWOON NN bu Environment of Forests See exercise 81 on page 714 Given the graph of a function f determine the intervals where f is concave upward and where it is concave downward Also nd all in ection points off if any See exercises 18 on page 729 Determine which graph is the graph of the function f with the speci ed properties See exercises 912 on page 730 1 Show that the function f x 2 1s concave upward wherever it 1s de ned x Determine where the function is concave upward and where it is concave downward a fx3 x lnx GNP x mmw x l Find the horizontal and vertical asymptotes of the graph See exercises 110 on page 745746 Find the vertical and horizontal asymptotes to the graph of the function wm x mnm j 2 x x Use the information summarized in the table to sketch the graph off See exercises 3336 on page 747 Sketch the graph of the function using the curvesketching guide x x2 4 a fx 2x3 15x2 36x 20 b fx Cost of Removing Toxic Pollutants See exercise 61 on page 750 Find the absolute maximum value and the absolute minimum value if any of the given function a gx x2 4x3 b fx x4 x3 2x2 3 on 2 3 c fx x 1 on 1 3 x Maximizing Pro t See exercises 49 and 51 on page 763 Minimizing Construction Cost See exercise 3 on page 775 Optimal CharterFlight Fare See exercise 15 on page 776 Chapter Revenue See exercise 17 on page 777 Verify that F x 2x2 is antiderivative of f x 4x Find the inde nite integral 3 3 3 a jindx c Jde e J6x x 2 xdx b jx dx d j1x2 x5dx r je 5x3dx Find fx by solving the initial value problem f x 3x2 6x f2 4 Cost of Producing Clocks See exercise 65 on page 793

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