Math 111 B & C --- Skills to Review for Midterm II

1. Be able to find a linear formula from an English description.

Phrases to watch for:

“…is a linear function of…”OR “…has a straight line graph…”

“Items sell for $p each” (interpret: TR is linear with slope p)

“It costs you $c to make each Item” (interpret: TC is linear with slope c)
”for each increase in order size by one item, you reduce the price by $d per item” (interpret: TR is linear with slope –d) (see WS 3 and 13)

2. Given a formula for distance D(t), find formulas for ATS(t) and for AS over an interval of specified length (WS 12)

3. Given a formula for price per item (in terms of q), you should be able to find a formula for TR(q).

4. Given a formula for TR(q), you should be able to find formulas for AR(q) and MR(q). Vice versa, given AR(q), know how to find TR(q).

5. Given a formula for TC(q), you should be able to find FC and formulas for VC(q), AC(q), AVC(q), and MC(q). Vice versa, given one of: FC and VC(q), or AC(q), or FC and AVC(q), know how to find TC(q).

6. If you have formulas for MR and MC and you want to find the quantity that maximizes the profit, set MR=MC and solve for q. (If you get two positive quantities, remember that the profit is maximized at the transition from MR>MC to MR<MC.)

7. Know when and how to use the vertex formula
   Some typical questions:
• Find the time/quantity at which <some quadratic function> is largest/smallest/highest/lowest/maximized/minimized.
  Give the “x”-coordinate of the vertex.
• Find the largest/smallest/highest/lowest/maximal/minimal value of <some quadratic function>
  Give the “y”-coordinate of the vertex.
• Find the largest interval on which <some quadratic function> is increasing/decreasing.

8. Know when and how to apply the quadratic formula (to solve quadratic equations in standard form: ax²+bx+c=0).

9. Know how to obtain the formula for profit given formulas for price per item and for average cost.

10. Understand that BEP is

i. The smallest value of AC(q)
(so, if AC is a quadratic in q, then BEP is the “y”-coordinate of the vertex)

ii. the “y”-coordinate of the point where AC and MC intersect.

11. Understand that SDP is:

iii. smallest value of AVC(q)
(so, if AVC is a quadratic in q, …)

iv. the “y”-coordinate of the point where AVC and MC intersect.

12. Know how to compute the average trip speed and the total distance traveled from a given linear formula of the instantaneous speed (WS 17)