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x f (x) is continuous everywhere, since 25x = 2 (90 x) when x = 40. Clearly, f (x) < 0 when x > 90. Hence, we may restrict attention to the interval [0, 90]. For 0 < x < 40, f (x) = 25x, and f (x) = 25. Thus, there are no critical numbers in the open interval (0, 40). For 40 < x < 90,

Metal oxide Metal Gate (G ) ~ p Drain (D) n+ Enhanced channel Substrate (B)

+ VGG _

f (x) =

Source (S ) (a) (b)

Fig. 4-7

Thus, x = 45 is a critical number. In addition, 40 is also a critical number since f (40) happens not to exist. We do not have to verify this fact, since there is no harm in adding 40 [or any other number in (0, 90)] to the list for which we compute f (x). We now construct Table 14-6: f (45) = 45 45 2025 (90 45) = (45) = = 1012.5 2 2 2 f (40) = 25(40) = 1000 f (0) = 25(0) = 0 90 90 f (90) = (90 90) = (0) = 0 2 2 The maximum yield per acre is realized when there are 45 trees per acre. Table 14-6 x 45 40 0 90 f (x) 1012.5 1000 0 0

In an n-channel MOSFET, the gate (positive plate), metal oxide lm (dielectric), and substrate (negative plate) form a capacitor, the electric eld of which controls channel resistance. When the positive potential of the gate reaches a threshold voltage VT (typically 2 to 4 V), su cient free electrons

Issue at Par When a corporation is organized, the charter will state how many shares of common and preferred stock are authorized. Often more stock is au thorized than is intended to be sold immediately. This will enable the cor poration to expand in the future without applying to the state for permission to issue more shares. When stock is sold for cash and issued immedi ately, the entry to record the security has the usual form: Cash is debited, and the particular security is credited. A corporation may accept property oth er than cash in exchange for stock. If this occurs, the assets should be recorded at fair market value, usually as determined by the board of di rectors of the company. Issue at a Premium or a Discount The market price of stock is in uenced by many factors, such as: 1. Potential earning power. 2. General business conditions and other prospects. 3. Financial condition and earnings record. 4. Dividend record. Stock will be sold at a price above par if investors are willing to pay the excess, or premium. The premium is not pro t to the corporation but

CHAP. 4]

are attracted to the region immediately beside the metal oxide lm (this is called enhancement-mode operation) to induce a conducting channel of low resistivity. If the source-to-drain voltage is increased, the enhanced channel is depleted of free charge carriers in the area near the drain, and pincho occurs as in the JFET. Typical drain and transfer characteristics are displayed in Fig. 4-8, where VT 4 V is used for illustration. Commonly, the manufacturer speci es VT and a value of pincho current IDon ; the corresponding value of source-to-gate voltage is VGSon .

14.7 Find the absolute maxima and minima of the following functions on the indicated intervals: (a) f (x) = 4x + 5 on [ 2, 3] on [ 1, 1] on [0, 4] (b) f (x) = 2x 2 7x 10 (d) f (x) = 4x 3 8x 2 + 1 on [ 1, 3]

VT (b)

Fig. 4-8

1/2 0