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
I don't really get this question but simply put, if you are in college syntax matters very much. (13-4) = 9 *(x-5) = 9x-45.. although in this case. since there isn't a bracket around 13-4. you'd multiply by the -4 first, giving you, 4x-20+30 =4x-10
Answer:
If is positive, then the parabola opens upward, so the function decreases on and increases on . But if is negative, then just the reverse
