Section 2.5

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1. (a) $1.418$

2. (b) $2$

3. (b) $\$ 51.28$

(d) If the producers raised the price above the equilibrium price, then demand would decrease while supply increased. With supply exceeding demand, the producers would eventually decrease the price.
If the producers lowered the price below the equilibrium price, then demand would increase while supply decreased. With the demand exceeding the supply, the producers would eventually increase the price.

(e) If the producers increased production, the supply curve would be higher and the equilibrium price would decrease.
If the producers decreased production, the supply curve would be lower and the equilibrium price would increase.

4. $125 \text{ yards } \times 250 \text{ yards}$

5. $\$ 10.00$

6. (a) No

(b) Yes, $-1$ is the minimum value of $h$ on $[-1, 2)$ .

7. (a) No

(b) Yes, because the Intermediate Value Theorem does not apply in this case since the Heaviside function is not continuous on $[-1, 1]$ .

(d) Yes; although the Extreme Value Theorem does not apply in this case (since $H$ is not continuous on $[-1, 1]$ ), that does not preclude $H$ from having maximum and minimum values on the interval.

9. Apply the Intermediate Value Theorem to the function $h(x) = f(x) - g(x)$ .

10. Apply the Intermediate Value Theorem to the function $g(x) = f(x) - x$ .

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Difference Equations to Differential Equations

Section 2.5

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