Answer:
x=1/3
Step-by-step explanation:
A function f is given as
in the interval [0,1]
This function f being an algebraic polynomial is continuous in the interval [0,1] and also f is differntiable in the open interval (0,1)
Hence mean value theorem applies for f in the given interval

The value

Find derivative for f

Equate this to -5 to check mean value theorem

We find that 1/3 lies inside the interval (0,1)
Answer:
The answer is 54 cubes.
Step-by-step explanation:
Answer:
Yes. It is a vector space over the field of rational numbers 
Step-by-step explanation:
An element
of the set
has the form

where
are rational coefficients.
The operations of addition and scalar multiplication are defined as follows:


The properties that
, together the operations of vector addition and scalar multiplication, must satisfy are:
- Conmutativity
- Associativity of addition and scalar multiplication
- Additive Identity
- Additive inverse
- Multiplicative Identity
- Distributive properties.
This is not difficult with the definitions given. The most important part is to show that
has a additive identity, which is the zero polynomial, that is closed under vector addition and scalar multiplication. This last properties comes from the fact that
is a field, then it is closed under sum and multiplication.