Intermediate Value Theorem: Suppose that f(x) is an arbitrary, continuous function on an interval [a,b] . If there exists a value L between f(a) and f(b) , then there exists a corresponding value c∈(a,b) , such that f(c)=L
f(x)=x3+4x−1
f(0)=−1f(1)=4
Since the function changes sign in the interval (0,1) , hence there exists a c∈(0,1) such that f(c)=0
the top is equal to the bottom so u take the top and add it with it's self 24 +24 and do the same with the sides 9+9 add them together to get 66
Answer:
a) 375
b) 7062.75 mm²
Step-by-step explanation:
b) We need to find the shortest possible width and length to get the smallest possible area.
To get the boundaries for 19.4, we go on to the next significant figure (the hundredths) and ± 5 of them.
The boundaries are, therefore: 19.35 - 19.45
As for the length, we can see they've added 5 units as the measurement is correct to 2 sig' figures, which is the tens.
And so, if we do as we did before, we go to the next sig' figure (the units) and ± 5 of them, we get the boundaries to be 365 - 375.
Now, we just multiply the lower bounds of the length and width to get the minimal/lower-bound area:
365 * 19.35 = 7062.75 mm²