business calc

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Author:
jillmray
ID:
73568
Filename:
business calc
Updated:
2011-03-17 21:18:50
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MARGINAL FUNCTIONS GRAPH DRWAING
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Description:
test 3 review
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  1. TO FIND THE SLOPE OF THE TANGENT LINE
    • 1) FIND THE 1ST DERIVATIVE
    • 2) PLUG X INTO THE 1ST DERIVATIVE
  2. TO FIND THE EQUATION OF THE LINE TANGENT TO THE SLOPE
    • 1) FIND 1ST DERIVATIVE
    • 2) PLUG X INTO THE 1ST DERIVATIVE TO GET THE SLOPE
    • 3) PLUG (X,Y) INTO THE EQUATION
    • (Y-Y1)= SLOPE(X-X1)
  3. TO FIND THE SLOPE OF THE TANGENT LINE THAT IS HORIZONTAL
    • 1) FIND 1ST DERIVATIVE
    • 2) SET THAT EQUAL TO 0 AND SOLVE
  4. TO FIND THE RATE OF CHANGE
    • 1) FIND THE 1ST DERIVATIVE
    • 2) PLUG IN THE NUMBER THEY ASK FOR
    • EX: START AT 6AM END AT 9 AM = 3 HRS
  5. TO FIND THE AVERAGE VELOCITY OVER AN INTERVAL
    • S(X+H)- S(X)
    • ___________
    • H
  6. TO FIND THE INSTANTANEOUS VELOCITY
    • FIND THE 1ST DERIVATIVE
    • PLUG IN THE NUMBER THEY GIVE YOU INTO 1ST DERIVATIVE
  7. TO FIND THE ACCELERATION
    • FIND THE 2ND DERIVATIVE
    • PLUG IN THE NUMBER THEY GIVE YOU
  8. TO FIND THE COST OF PRODUCING THE 101ST ITEM (COMPUTE THE AVERAGE RATE OF CHANGE)
    • C(101)- C(100)
    • ____________
    • 101-100
  9. TO FIND THE MARGINAL COST OF PRODUCING 21ST ITEM
    • 1) FIND THE 1ST DERIVATIVE
    • 2) SUBTRACT 1 FROM THE NUMBER THEY GIVE YOU AND PLUG IN
  10. TO FIND THE AVERAGE COST FUNCTION AND AVERAGE COST
    • 1) DIVIDE THE ENTIRE FUNCTION BY X
    • 2) PLUG IN THE NUMBER THEY GIVE YOU WHERE THE X'S ARE LEFT
  11. TO FIND THE REVENUE FUNCTION R(X)
    MULTIPLY THE FUNCTION BY X
  12. TO FIND THE MARGINAL REVENUE FUNCTION AND MARGINAL REVENUE
    • 1) FIND THE FIRST DERIVATIVE OF R(X)
    • 2) SUBTRACT 1 FROM THE NUMBER THEY GIVE YOU AND AND PLUG INTO THE 1ST DERIVATIVE
  13. TO FIND THE PROFIT FUNCTION P(X)
    • P(X) = R(X) - C(X)
    • 1) TO FIND R(X) MULTIPY p(x) BY X
    • 2) THEN SUBTRACT R(X) BY C (X)
  14. TO FIND THE MARGINAL PROFIT FUNCTION AND MARGINAL PROFIT
    • FIND THE 1ST DERIVATIVE OF P(X)
    • SUBTRACT ONE FROM THE NUMBER THEY GIVE AND PLUG IT IN
  15. TO FIND IF INCREASING OR DECREASING
    • 1) FIND THE 1ST DERIVATIVE
    • 2) FACTOR IF POSSIBLE
    • 3) SET EQUAL TO 0
    • 4) DRAW THE LINE GRAPH WITH X'S AND TEST POINTS
    • 5) PLUG IN TEST POINTS TO 1ST DERIVATIVE
    • 6) IF ITS NEGATIVE <0 THEN ITS DECREASING
    • IF ITS POSITIVE >0 THEN ITS INCREASING
  16. TO FIND THE RELATIVE MIN OR MAX (EXTREMA) OF A FUNCTION
    • 1) find the 1st derivative
    • 2) factor if possible
    • 3) set equal to 0
    • 4) draw the line graph with x and test point
    • 5) plug into the 1st derivative
    • 6) if its negative then its relative min
    • if its positive then its a relative max
    • 7) to find the y value for the point plug into the ORIGINAL FUNCTION
  17. TO FIND CONCAVITY
    • 1)FIND THE SECOND DERIVATIVE
    • 2) FACTOR IF POSSIBLE AND SET EQUAL TO 0
    • 3) PLOT THE POINTS AND TEST POINTS ON NUMBER LINE
    • 4) PLUG TEST POINTS INTO F"(X)
    • 5) IF NEGATIVE THEN CONCAVE DOWN
    • IF POSITIVE THEN CONCAVE UP
  18. TO FIND POINTS OF INFLECTION
    • 1) FIND THE SECOND DERIVATIVE
    • 2) FACTOR IF POSSIBLE AND SET EQUAL TO 0
    • 3) PLOT THE POINTS AND TEST POINTS ON NUMBER LINE
    • 4) PLUG TEST POINTS INTO F"(X)
    • 5) IF THERE IS A CHANGE IN THE SIGN AS YOU MOVE ACROSS THAT POINT THEN ITS AN INFLECTION POINT
    • 6) IF YOU NEED THE Y COORDINATE PLUG THE X'S INTO THE ORIGINAL FUNCTION NOT THE DERIVATIVE
  19. IF e to the x is raised to a negative #
    e^(-x) then
    its positive >0
  20. IF E TO THE X IS NEGATIVE -e^(X) THEN
    • ITS NEGATIVE REGARDLESS IF THE X IS NEGATIVE OR POSITIVE
    • <0
  21. THE SECOND DERIVATIVE TEST
    • 1) FIND THE 1ST DERIVATIVE
    • 2) FACTOR F'(X) AND FIND THE X VALUES
    • 3) FIND THE SECOND DERIVATIVE
    • 4) PLUG THE X VALUES YOU FOUND INTO F"(X)
    • 5) IF ITS EQUAL TO 0 THEN ITS INCONCLUSIVE
    • IF ITS >0 ITS A RELATIVE MIN
    • IF ITS <0 ITS RELATIVE MAX
    • 6) TO FIND THE Y VALUE PLUG THE X VALUES INTO ORIGINAL FUNCTION NOT THE 1ST OR 2ND DERIVATIVE
  22. STEPS TO CURVE SKETCHING
    • 1)DETERMINE THE DOMAIN OF F
    • 2) FIND THE RATIONAL X INTERCEPTS
    • 3) DETERMINE THE END BEHAVIOR
    • 4) DETERMINE WHETHER INCREASING OR DECREASING
    • 5) FIND X AND Y COORDINATES OF ANY EXTREMA
    • 6) DETERMINE WHERE ITS CONCAVE UP OR DOWN
    • 7) FIND THE X AND Y COORDINATES OF POINTS OF INFLECTION
    • 8) PLOT MORE POINTS IF NECESSARY
    • 9) 10 SKETCH
  23. ODD DEGREE POSITIVE LEADING COEFFICIENT
    LEFT END IS DOWN RIGHT END IS UP
  24. ODD DEGREE NEGATIVE LEADING COEFFICIENT
    LEFT END IS UP RIGHT END IS DOWN
  25. EVEN DEGREE, POSITIVE LEADING COEFFICIENT
    BOTH SIDES ARE GOING UP
  26. EVEN DEGREE NEGATIVE LEADING COEFFICIENT
    BOTH SIDES ARE DOWN

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