I'm not sure exactly which type you are meaning since there are four types of expansions, but depending on which specific type here are your answers! :)
20 shares at 10 1/2 (or 10.5) = 20 * 10.5 = 210
20 shares at 11 1/4 (or 11.25) = 20 * 11.25 = 225
so the profit made would be : 225 - 210 = $ 15 <==
F(x) is continuous for all x.
Pick a point and show that f(x) is either negative or positive. Pick another point and show that f(x) is negative, if positive, or positive, if negative.
At x = 30, f(30) - 1000 = 900 + 10sin(30) - 1000 ≤ 0
Now, show at another point f(x) - 1000 is positive, and hence, there would be root between 30 and such point.
Let's pick 40.
At x = 40, f(40) - 1000 = 1600 + 10sin(40) - 1000 ≥ 0
Since f(x) - 1000 is continuous, there lies a root between 30 and 40, and hence, 30 ≤ c ≤ 40
