Answer:
The proof is detailed below.
Step-by-step explanation:
We will first prove that if H(x) is a differentiable function in [a,b] such that H'(x)=0 for all x∈[a, b] then H is constant. For this, take, x,y∈[a, b] with x<y. By the Mean Value Theorem, there exists some c∈(x,y) such that H(y)-H(x)=H'(c)(x-y). But H'(c)=0, thus H(y)-H(x)=0, that is, H(x)=H(y). Then H is a constant function, as it takes the same value in any two different points x,y.
Now for this exercise, consider H(x)=F(x)-G(x). Using differentiation rules, we have that H'(x)=(F-G)(x)'=F'(x)-G'(x)=0. Applying the previous result, F-G is a constant function, that is, there exists some constant C such that (F-G)(x)=C.
Answer:
$48.60
Step-by-step explanation:
50(.10)=5.00 50-5=45. 45(.8)=3.60. $45.00+$3.60 = $48.60
Answer:
well when you hear "union" you think 'joined' or 'together' since thats what it means, In a mathmatical set of numbers, union means that both of the sets are necessary for the equation to be true. I'm not sure what the sets are in this problem but in order to get "union" from anything, that means that when you checked for your domains, the values that you got had to be part of both the given sets
#4. 20 Tropical Fantasies
Answer:
70
Step-by-step explanation:
70 has the greatest absolute value because absolute value is the amount between that number and 0. If 70 is the biggest number the with the biggest absolute value is 70.